Hello everyone and welcome to this presentation where we are going to be talking about United Nations peacekeeping and today we are presenting a dataset of tasks which appear in UN peacekeeping mandates and I'm very happy to welcome my co-authors on this project and today we have Jessica Dyselvatore who is Associate Professor in Political Science and Peace Studies at the University of Warwick. We also have Magnus Lundgren, Associate Professor in Political Science at the University of Gothenburg and we have Hannah Schmidt who is Head of Research Area on International Security, Peace and Conflict at the University of Zurich. And the goal of our presentation today is to discuss this new dataset that we have created which has coded the tasks assigned to peacekeeping mandates of UN peacekeeping operations in Africa, covering pretty much all of the post-Cold War period starting in 1991 and going up to 2017. And in general in the policy literature and the academic literature as well there has been a lot of discussion about the changing character of peacekeeping and at the beginning of this presentation I will talk a little bit about the decision-making process behind peacekeeping mandates and I will talk about some of the major changes in the practice of peacekeeping before we get into more detailed discussion of how tasks have actually changed over time which is something that our dataset will hopefully illuminate. And in terms of housekeeping our presentation will hopefully not exceed 40 minutes which will leave ample time for online seminars and this presentation is being recorded so I hope that everyone is okay with that and it will be uploaded so people can view it later as well. And both the presentation and the questions and answers session will be recorded and if you want to ask a question from you know on any topic related to our presentation to any of the panelists please use the Q&A box I hope you can all see it on your screen and after we have completed our presentation I will wonder rate the questions and answers session and we will try to answer all of your questions if we have time. So please use the Q&A box instead of the chat box because it will be easier for me to moderate. Okay all right so as I've mentioned I will start this presentation by discussing some of the major changes in the practice of peacekeeping as well as peacekeeping decision making. Yeah so I have found some photos which illustrate how peacekeeping has changed from its Cold War origins to its contemporary shape and form. So on the picture on the left we can see a peacekeeper in the Yuan peacekeeping operation in Cyprus in the year 1965 and we can see that this peacekeeper is manning an observation point he has a binocular he's lightly armed he is engaging in what peacekeepers would call static guard duty and the main goal of such operations was monitoring observing and reporting on various developments and Cold War operations were usually deployed in interstate conflicts of course there have been exceptions the practice of peacekeeping has never been uniform but most peacekeeping operations during the Cold War followed this model which is usually called the traditional peacekeeping model and we can see that the goal of those operations was confidence building between parties that have signed a ceasefire agreement sometimes a peace agreement and on the picture on the right we see the contemporary form of peacekeeping and to be honest I would probably not even know that it was a peacekeeping operation these are Canadian forces deployed in Mali and we can see that everything has changed their gear has changed they are much more heavily armed they operate as cohesive units they rely on various assets technological assets aviation assets and we know that in Mali peacekeepers engage in what is called robust operations they operate in a difficult environment they face various types of threats threats from armed groups threats from improvised explosive devices and it's just just a very different peacekeeping setting and I think these two pictures illustrate that the tasks objectives mandates of peacekeeping operations have really changed over time but we have found that this discussion about peacekeeping becoming more robust or more multi-dimensional has lacked specificity because we know that peacekeeping has changed but we haven't had a comprehensive overview of how peacekeeping has changed and of course many of those changes have happened in the post-Cold War period many of the tasks which emerged at the end of the Cold War focusing on supporting transitions to democracy focusing on elections focusing on engagement with the civilian population they have really grown in terms of their number and diversity over the last 30 years and of course peacekeeping remains a military affair at its heart but at the same time the number of various civilian tasks has increased and on these pictures we can see that peacekeepers engage in a wide variety of activities besides the tasks that military components do although some of those tasks are also responsibility of military components so on the picture on the left we can see peacekeepers again in Mali delivering a training on minor awareness and various activities related to demining have been a persistent feature of peacekeeping operations throughout the post-Cold War era but this is just one type of training that peacekeepers deliver to the civilian population there are also other kinds of training and education and engagement and confidence building at the local level that peacekeepers can engage in and then there are two pictures on the right and the picture on top is a picture of a journalist from the radio station in the Central African Republic which is run by a peacekeeping mission and since the UN mission Cambodia many peacekeeping operations have had a radio station which can be a very effective tool in terms of spreading awareness of the mission itself and of the peace process and on the picture on the bottom we can see military peacekeepers guard in a polling station in the Central African Republic and it is a part of their electoral security mandate which has also become an important element of peacekeeping and we will talk in more detail about patterns in various tasks assigned to two peacekeeping mandates but before we do that I would like to say a few words about how peacekeeping mandates are negotiated so peacekeeping mandates are negotiated by the UN Security Council which is one of the principal organs of the United Nations it's a body that consists of five permanent members the US the UK France Russia and China and 10 non-permanent members that serve two-year terms on the council and they're elected and the UN Security Council collectively initiates peacekeeping operations it can make a decision to launch a new peacekeeping operation it also assigns the mandate in the form of the list of tasks to a peacekeeping operation it also sets a ceiling the maximum size of the military and police component of the peacekeeping mission and then usually yearly sometimes every half a year it revises and amends the mandate and we're looking at revised and amended mandates of peacekeeping operations because some missions stay in the field for decades for example the UN mission in the Democratic Republic of the Congo is now in its 21st 22nd actually 22nd year so I think it's important to look at initial and amended mandates and in terms of the process of peacekeeping negotiations these negotiations are led by in the contemporary era they are led by one of the permanent members one of the western permanent members so each of those three western members has a responsibility for a particular portfolio for a particular conflict situation for example France is the lead on the peacekeeping operations in Mali the Central African Republic the Democratic Republic of the Congo and Lebanon the US leads on South Sudan and the UK leads on Cyprus and in order to adopt a peacekeeping resolution and you are an amended peacekeeping mandate nine affirmative votes are necessary and no vetoes and for most of the Cold War period peacekeeping negotiations haven't been very contentious it was usually not very difficult to reach consensus of course with some prominent exceptions like the missions in the Balkans which were quite contentious but a trend in the recent period is that some of the more consensual tasks like those related to human rights or the women peace and security agenda have become more and more contentious so we think that it's important to look at peacekeeping mandates especially at the desegregated level at the specific tasks which appear in new and revised peacekeeping resolutions and this was one of our motivations in creating this data set thank you Xenia to add on what Xenia has already told you all I would like to elaborate a little bit more on why we are motivated to study the content of peacekeeping mandates and to add on what Xenia has already elaborated on one other reason is that mandates have gotten a lot of attention from different stakeholders of UN peacekeeping operations lately and this might be because of what Xenia has been already referring to there is anecdotal evidence that suggests that mandates include many more and many more diverse tasks ranging what Xenia has said from security sector reform to election assistance to facilitating reconciliation with ordinary people on the ground and there is a debate whether these increasingly complex mandates are a good thing or a bad thing so on the one hand the UN secretary general Antonio Guterres pleaded please put an end to mandates that look like Christmas trees Christmas is over he said and the UN mission cannot possibly implement 209 mandated tasks and he continued to say that these unrealistic demands due to the complexity of mandates put on peacekeeping operations will cost lives and will hurt the credibility of UN peacekeeping operations as well as the UN as a whole on the other hand there are also arguments in favor of Christmas tree mandates or at least not not against Christmas tree mandates some scholars argue for instance that paring down peacekeeping mandates so streamlining them and reducing the number of tasks and peacekeeping mandates comes with a risk for peacekeepers namely the risk of losing flexibility in their theater of operation the flexibility of picking and choosing the tasks that the most appropriate in a given situation so despite this increasing attention and debate about the increasingly complex Christmas tree mandates we actually have little systematic analysis of how mandates actually look like which tasks do UN security council mandates request from peacekeepers how do number and composition of tasks change over time and vary across host countries of peacekeepers and in our project we seek to answer these questions by collecting data on the task in peacekeeping mandates and how they have changed over the lifespan of the missions and of course we are not the first ones to do so there have been efforts to collect data on peacekeeping mandates so there are the early quantitative study that broadly distinguish between traditional security focused missions a picture of that Xenia shown you at the beginning and on the other hand multi-dimensional missions with mandates and mandated tasks that seek to transform the political social and economic environment in peacekeepers host countries yet today as Xenia has already said most missions are multi-dimensional so hence we need more fine-grained data on mandated tasks in order to distinguish between the different types of multi-dimensional mandates and missions and take a closer look at what tasks multi-dimensional missions are actually mandated to carry out and there have been efforts to collect data on these multi-dimensional tasks for example Govinda Clayton, Han Dorsen and Tobias Böhmelt have recently recorded some functions of peacekeepers including election assistance and security sector reform but the tasks that they coded in their UN peace initiatives dataset are not comprehensive of all the tasks that peacekeeping mandates contain and one reason for that is that they also look at other peace efforts and the mandates of other peace efforts such as sanction committees mediators tribunals and investigative bodies and then there have been four studies that we could identify that focused specifically on the mandates of UN peacekeeping operations however they also only code a few selected tasks and they are by no means comprehensive of the 209 mandated tasks that Antonio Gutierrez identified in the Christmas tree mandates of today. Moreover with the exception of the task assigned to mission mandates by Gabi Lloyd from 2020 all the existing efforts to collect data on peacekeeping mandates focus on initial mandates that establish a mission and just they just capture a snapshot of the mission. They do not code how mandates evolve over the lifespan of mission deployment and since as Xenia has already mentioned peacekeeping operation nowadays can stay for decades we also want to know how their mandates change over the lifespan of the mission. So considering these existing efforts to collect data on peacekeeping operations we think there are still three blind spots spots and three contributions that we can make with our dataset on peacekeeping mandates tasks. So first of all existing efforts have not comprehensively recorded and the task and the tasks are at a high level of aggregation for example all existing peacekeeping mandate datasets only record security sector reform as one task whereas our dataset disaggregates security sector reform into six different tasks namely police reform, military reform, justice sector reform, transitional justice, prison reform and legal reform. Furthermore our dataset also codes the modalities of engagement with respect to the different tasks. Existing datasets all but ignore these modalities of engagement ignore what exactly peacekeepers should do with respect to the task and in contrast to that our dataset codes whether mandates request peacekeepers to monitor a given task or to assist with a given task or to secure a task and we also distinguish whether mandates request demand from peacekeepers to carry out the task or merely encourage the tasks. And finally as already mentioned our dataset also codes variation over time which is all but ignored in the existing efforts except in the dataset by Gaby Lloyd. So we also we do not only code initial UN Security Council resolutions but also resolutions that change the mandates of the peacekeeping operations. In total we have coded 386 resolutions from 1991 to 2017 for 27 peacekeeping operations in Sub-Saharan Africa and here you see the beginning of the initial UN Security Council resolution that established the currently youngest peacekeeping operation in the world, the operation in the Central African Republic. And this initial resolution reads that the UN Security Council decides to establish the United Nations multi-dimensional integrated stabilization mission in the Central African Republic as of the date of the adoption of this resolution for an initial period up to like one year. And then we also code a UN Security Council resolutions that extend the mandate of an existing resolution like the one shown here again for MINUSCA and this resolution reads that the UN Security Council decides to extend the mandate of MINUSCA for another year. And finally we code those mandates that change the content of the mandate of an existing operation for example this resolution here from 2016 which decided that the mandate of MINUSCA shall include the following immediate priority tasks and this resolution then specifies a new set of tasks that should be the immediate priority of the MINUSCA mission for example civilian protection and local reconciliation initiatives. We code from these resolutions a comprehensive set of tasks and we have identified these tasks by a close initial reading of the mandates. And then based on our reading we have continuously added to a list of tasks and we arrived in total at 39 different tasks. And here you see a list of the mandated tasks we have coded so we code tasks that seek to establish some level of agreement between the literate parties and that are ceasefire and peace process assistance, we code humanitarian relief including for refugees, we code tasks that are related to democratization and election processes, we code DDR tasks, re-record tasks related to cursive peacekeeping and of course we code the cross-cutting tasks related to human rights and gender that the UN secretariat want to see mainstreamed into all other tasks of the mission. Moreover we code control of arms and demilitarization and then we code a host of rule of law tasks including security sector reform and also assistance to media and civil society. We also distinguish between five state authority extension tasks and finally we code tasks that aim at reconciliation and restoration of relations within society and relation between the host state and other states in the region. And after we had coded all these tasks from the resolutions we realized that they neatly fit with the broader task categorization by Paul Deal and Daniel Druckmann and we take this as an additional indicator for the validity of our coding scheme that these tasks that we have identified actually resonate with what scholars think are the relevant tasks in peacekeeping mandates. But yet again you can see our coding our categorization of tasks is much more fine-grained for example we have identified resolutions that only mandate disarmament and demilitarization and other that also mandate reintegration and we distinguish these mandates. As already mentioned we also code modalities of engagement, are peacekeepers merely requested to monitor a task or are they also asked to assist with a task or shall peacekeepers secure a task? So for example you see evidence from the UN Security Council resolutions for all three modalities with regards to the task of disarmament and demilitarization. So evidence from a Security Council resolution for monitoring would read as follows contribute to the implementation of the national program of disarmament demilitarization and reintegration by monitoring the disarmament or a UN Security Council resolution mandating peacekeepers to assist with DDR could read request the secretary-general to appoint expediously a special representative who shall coordinate the overall support of the international community in Mali including in the field of disarmament and demilitarization. And evidence for securing a task such as disarmament demilitarization could read to provide security in and at all sides of the disarmament demilitarization and reintegration program. Beyond that as already mentioned we also distinguish between whether the UN Security Council resolution requested engagement in an area or just encouraged engagement. Before I've read out evidence for requests here is also evidence for when the UN Security Council encourages the task which reads calls up on UNMIS to coordinate with the government of the Republic of South Sudan to support disarmament demilitarization and reintegration efforts. So calls up on here is the keyword for encouraged engagement by the peacekeepers in the DDR process. We have coded all resolutions ourselves and each resolution was coded twice that means that two of us have read and recorded the task mentioned in these resolutions independently and afterwards we have then discussed our coding decisions and reconciled differences in our codeings. And this means we are sure about the validity and reliability of our coding in accordance to our code book. So overall we think that our data quality is very high. And with that I would like to hand over to Magnus who will show you some descriptors of our dataset. Thank you very much Hannah. So building on what Xenia said about the background and what Hannah said about the motivation and the construction of the data I'll present very briefly some of the content of the data what it looks like to provide some meat to these conceptual bones. And it has been stressed that data is comprehensive and finally granular so it can be cut up in different ways. Now I'm going to cut it up in two different ways both focusing on macro patterns so pertaining to variation across mission over long periods of time but also pertaining to micro patterns so variation within missions from resolution to resolution. And you'll see that both of these cuts show that there's considerable diversity in mission mandates. Next slide please. Thank you. So first I'm turning to macro patterns this figure shows the content of mission mandates at the point of mission establishment. So we have missions on the x-axis in the figure going from Minerso in 1991 that's the first mission that's coded in our data all the way up to Minusca in 2014 that mission was established. And then on the y-axis we have the different tasks here they are grouped into three larger categories a category of stability related tasks a category of peace building widely construed a related task and a category of rights tasks. And if a particular mandate of a mission at its establishment incorporates or specifies a given task it's marked in dark gray if it's not included in the mission mandate it's marked in light gray. So this provides a bird's eye overview of the development of peacekeeping mission mandates between 1991 and 2014. And in the paper we well that goes with the data set we have identified three macro patterns these are patterns that have been discussed in the literature before so they're not necessarily novel insights but what we can do on the basis of our data is to provide systematic data to support these insights and to to show more exactly how they have played out. And the first is a growth in scope of mandates this has already been referred to in this presentation we see that mandates get longer and longer they they include more and more tasks whereas missions in the early part of our period so in the early 90s had a handful of tasks and someone sometimes only one or two tasks missions established more recently so after the turn of the millennium in particular have 15 or 20 or sometimes even more tasks so we see expansion of tasks or in the number of tasks and that development is driven by two other transfer patterns which are also listed on this slide as number two and three and the second one is we see an expansion of peacekeeping mandates into new policy areas a way in particular from from the pre or Cold War Area traditional type of peacekeeping and this so we add so so the Council the Security Council adding new tasks that were not included in earlier in the mandates of earlier missions and this relates in particular to the enhancement of state capacity economic development and to rights you can see for example in the figure here how rights related tasks are nearly non-existent in the missions in the left hand half of the figure but are routinely assigned to missions of a more recent mark so those are the three macro patterns that emerged from our data more tasks newer tasks and and also the thirdly then I should say disaggregation of tasks so we see that tasks that were are split up into to a greater number of tasks for example security sector reform has been split up into a number of more refined or more specific tasks such as police reform or military reform that's the third so those are the three macro patterns that we see in the data if we turn to micro patterns in the next slide we can see what this looks like for specific missions again because the PMA data is so highly granular with observations on individual missions resolution by resolution we can do a similar type of analysis for individual missions to really get into the granular nature of how they evolve over time and the figure here shows the mandate or mandates if you want of the missions in the DRC Monuc and Monusco Monusco being the follow-on mission of Monuc from the first resolution 12 179 which was adopted by the council in November 1999 to resolution 2348 which was adopted in March of 2017 again we have the tasks on the y-axis and again we see that the the quite a lot of diversity over time in in the tasks that the council wants this mission to carry out and this reflects then how the the council has negotiated mandate then renegotiated it and in through this extension also amendments the mandate adding tasks dropping tasks sometimes replacing one task with another task and so on and we have identified if we go to the next slide which is just an add-on onto this slide six different phases that this mission goes through you can cut this differently but we identified six phases to then categorize the development over time in the first phase Monuc was a very small mission few few personnel and only a very short list of core tasks and it has then in reflection of negotiations and security council evolved through these different phases with the the mandates stipulated by council changing as a response to that you can see for example between phase two and three how the council adds a number of tasks for example justice secretary reform is added in phase three and then dropped in phase four only to reemerge again in phase five so the takeaway here is that there's quite a lot of longitudinal variation within missions adding to the diversity of variation that we saw in the previous slides of variation across missions so if we are interested in diversity in mission mandates which we should be and we think is it's a relevant research topic for various reasons this type of data is an important resource and i'll hand over to jesse we can now tell you more more specifically what the data can be useful thank you thank you very much so in case you're still wondering why this data is useful why you need data on your mission mandates but we're standing at the very convincing point that Stenya Hanna and Magnus said already raised so let me let me maybe mention a couple that we think a couple of research strands that we think can particularly benefit from this data and so to begin with probably the one of the most obvious to those that study peacekeeping operations and their impact on the ground concerns the possibility of thinking of mandate as documents that design specific conflict management tools so if you think of peacekeeping as a conflict management tool you may want to see which are the different components of that tool that allow the tool to ultimately work or fail right so you can think of different aspects of peacekeeping you may want to study and more specifically actually different reasons to focus on the mandates of these peacekeeping operations for example you can think of the possibility that the fact that a single task is included in a mandate may be itself a signal of commitment right so it may just show that the UN or the international community or the troop contributing countries are more committed to those specific tasks which in turn suggests that missions that are kept with different mandates may perform differently on the ground I think this is a question that ultimately requires we would we could say an empirical answer in the sense that you can assume that mandates make a difference but you need to maybe you may want to verify that we want to check whether that's the case and whether this inclusion of a specific task alters the performances of the missions on the ground and finally we also knowledge of course the possibility that peacekeepers may go beyond the mandated task or may not perform at all what's in their mandates but we also think that because of the reasons that Xenia mentioned when she described how these documents were negotiated the role of the pen holders there's still a degree of legitimacy attached to these documents and the expectations that peacekeepers on the ground in a way will stick to the mandates and again it is another type of question that needs to be studied more empirically and for which you do need this type of data you need to understand where you need to you need the level of granularity that allows you to really see whether this makes any difference on the ground and also whether that affects the even the perceived legitimacy of the actions that peacekeepers do on the ground particularly when we think about tasks that may be perceived as particularly intrusive because maybe they deal with political reforms the presence of experts and advisors that are usually work assist the government so for some tasks we believe that these elements this element of the legitimacy is particularly relevant and so this is the first trend of research that that we think will particularly benefit from the data there's also another one which relates a weather on which relates to the study of international relations international organizations as a whole so again to reiterate the point mandates are the result of negotiations and looking at what ends up in a mandate it does tell you something about maybe the whole negotiation process and maybe also the normative priorities and the trends that make assist in international organizations of course in this case we're focusing specifically on the UN case which is maybe for many the paramount international organizations so this I think can also give you an insight into which are yes these normative priorities think about tasks that were never mentioned in the past like Magnus has mentioned so the introduction of human rights in the mandate as a task that we see more and more often included in these documents and in addition you can also consider evaluating internal and external factors that shapes the debate and ultimately the design of the finally authorized mandates and also the relationship between the different bureaucracies within the UN because the whole negotiation process also involves recommendations by the secretary general that goes to the security council and Magnus thinks that I have this very interesting paper on global governance where they see at the conditions at how likely the security council is to accept those recommendations and without knowing what ends up in a mandate you really cannot do the type of research and you cannot believe reveal the those patterns and these dynamics that exist that are specific to international organizations now what do we do with Pima though so in the working paper we examine an existing study that focuses on the first strand of research so peacekeeping effectiveness so to speak do peacekeepers save lives and more specifically we re-examine this work on the American Journal of Political Science by Lisa Altman, Jacob Kaplan and Megan Shandan was published in 2013 and ultimately the conclusion of the paper is that sizable deployment of UN of armed UN peacekeepers so military presence visible military presence by the UN saves civilian lives on a monthly basis so you see a reduction in the number of civilians that get killed in host states when there is a sizable presence of armed peacekeepers so this is the finding of the paper and we just asked another question on top of that we asked do mandates make any difference on the ground so do we see any difference if we try to understand it's possible for example that if a mandate allows peacekeepers to protect civilians explicitly this gives legitimacy to more proactive actions that peacekeepers may sometimes need to take when they need to offensively for example react offensively take action against violence and violations perpetrated against civilians or in addition the presence of the task makes self that are escalation because it's signal the willingness to respond and finally exactly because Pima allows us to make the distinction between monitoring and actively protecting civilians we are also able to see whether the the new inclusion of the task as a token is enough or whether you need to ask peacekeepers require peacekeepers to actively protect civilians on the ground and this is definitely one thing that Pima allows us to do so a few things that I would like to point out in our reexamination which is not a replication exactly because we aim at looking at something that is different we rely on that paper as our baseline so to speak and then we add something else on top of that which is why we ultimately reexamine those findings so Osman Kathman and Shandon in fact did include in one of their models a measure of POC protection of civilian mandates however they do so by only coding whether that was included in the mandate that authorized the mission in the first place so basically there's no information on temporal changes for example whether the mandate was in the task was included in later stages for example so that information is basically lost it's a variable that never changes it's a constant for all the missions that they have in their sample and in relation to the sample we exclude Binup and UNOA because these are special political missions which we do not include in our sample that is a sample of peacekeeping operations so for the moment these are those that we are coding and the reason why these these missions actually end up in their data set is because at some point they do host troops which means that they end up in the data set and so they have it there for for this reason so what we want to explain with this model is whether including POC tasks related to a protection of civilian in mandates changes the number of civilians that get kids on a monthly basis using the UCDP data so the model is exactly the same as the one that they propose we use exactly their specification with the only difference that we add another variable which is protection of civilian mandates as I said and we code this in a couple of different ways so we first just code whether the mission includes whether the mandate includes at a certain point in time a task to a task to protect civilian a task for the mission to actively protect civilians so they need to be requested to either assist the government in protecting civilians or to protect civilians regardless of what the government decides to do and so this is a distinction that our levels of engagement and strength of the provision allow us to make and we further play with the distinction by coding other two variables which which distinguish protection of civilians that is active which means the mission again is similar to what I just said basically so the mission is requested to act to protect civilians and passive protection of civilians where the mission is asked to either monitor civilians or whether they are just monitoring if any violations of monitor and reports oftentimes whether any violations of course against civilians or encourages the mission to protect civilians or vulnerable vulnerable groups so it's a more soft softer provision we would say so this is how we measure that and just to give you an overview of our main findings so here you can see the different effects of the different variables included in our models on top you have u n troops so this the the the the the dash the dash line uh it's basically it's centered at zero so everything that is on the left side suggests that that variable has a negative effect meaning it reduces civilian killings so it's a good thing because it saves lives everything that is on the right hand side suggests that actually the opposite is happening however if anything crosses the the dotted line it just means that you cannot conclude anything because results are basically statistically non-significant you cannot distinguish the effect from zero that's the ultimate understanding here so if you just give a glance at this graph what you can see is that u n troops as it as the main finding of hks suggests seems to reduce variance against civilians on a monthly basis so this finding remains and you can only also see that the protection of civilians the the row two and three where we compare the way hks measure that and how we measure that with pima are pretty similar in size they do not change substantively really the key difference uh really materialize one to distinguish passive and active peacekeeping it seems that most of the of the job here is made by i'd actually asking peacekeepers to protect civilians so it's not enough to just add tasks that refer to protection of civilians to make a difference on a difference on the ground ultimately and as an additional set of models that we show we also distinguish one-sided violence perpetrated by the government and perpetrated by the rebels and here we so we don't want to over interpret this because we just want to be examining the baseline paper that the people by hks but we just want to briefly maybe also draw this distinction here so just to summarize this very quickly if you look at the rebels side on the on the yeah the violent side here rebel sponsored violence it's still reduced by the presence of u and troops so military presence seems to deter violence against civilians perpetrated by the rebels but mandates do not really seems to make a difference anymore which might make sense if you want to think of rebels maybe not being necessarily aware of the content of the mandate or maybe because they do need to have a visible military sizable military deployment to actually to actually be the third and not use violence against civilians so this is possible interpretation of course we know exactly know whether this is the case but if we ask me how we how we interpret that this would be i think our our answer any opposite happens when you focus on the government on the left hand side so you see that troops here really cross the dashed line which means that governments are not necessarily deterred by the presence of large military deployments but they do reduce the reliance on one side of violence so violent against civilians when the muddend includes provisions to protect civilians and more specifically when you disaggregate passive and active protection of civilians you see again that actively protecting civilians provision of this type included in the mandate reduces the the lack the the number of civilians that get killed by the government but just including active passive protection of civilians hence a less robust version of that we could say seems to actually backfire in a way and let me tell you that what what this may sound surprising this is actually in line with other findings suggesting that when you and the ploys observers which are not armed the balance perpetrated by the government tends to increase so you can think of the deployment of observers that are unarmed and ultimately not really a military deterrent something maybe that it's doing the same thing as just asking encouraging peacekeepers to protect civilians so very briefly to summarize it seems that based on these reexamination the balance reducing effect of protection of civilian mandates is largely due to the active protection of civilian tasks presented in the mandate and rebels seems more responsive to military deployments than to the content compared to the content of the mandate when the opposite seems to be true for government and we do have also this interesting findings for the disaggregate passive and active protection of civilians so maybe to conclude let me mention maybe another couple of ongoing work that some of us are are carrying out at the moment that I think would have really wouldn't have been possible without female ultimately so it's really something that only was made possible by the fact that this data became available at some point so that we collected it so with Anna Schmidt here and Rob Blair from University of Brown we're working on this paper that looks at the conditions that allows peacekeeper operations to actually carry out the very same activities that they are mandated with so basically we try to see what what enables peacekeepers to match the ambitions of the mandate and the activities that they then carry out on the ground in another paper with Katja Kohleman, Xenia Oximitna and Sabin Otto a very newborn idea where we try to look at whether this new mandate that seems to be more civilian oriented at least in the tasks that they include are also matched with similar resources on the ground so whether that corresponds to the type of stuff that UN is willing to invest in so do they hire more civilian staff is the civilian stuff more likely to be deployed to those missions that do have those civilian oriented tasks and finally another paper by Anna Schmidt with Sabin Otto and Constantine Vru where they look more specifically at human rights activities and again what makes peacekeepers more likely to engage with activities and they formulate this idea that it's possible that of course having a mandate to do so may increase the possibility that this happens but it's also important to look at how the mandate as a whole look like so whether there's a space actually for peacekeepers to carry out those specific tasks and I will leave it there thank you so much for your interest and we look forward for your questions thank you thank you very much to Jessica Magnus and Hannah for their fantastic presentation I hope that it was quite comprehensive showing showing us what this data can do how it can be used and how it can further our understanding of peacekeeping we have 40 minutes for questions and answers which is really great I know that unfortunately Magnus will have to believe us at some point because he has another meeting which was impossible to move but we will try to pick up all the questions that you might have and I will start with questions in the Q&A box please use the Q&A box to post them and then I'll move on to the chat to pick up some questions there so in terms of the questions in the Q&A box there is a question about mine action so mine action related tasks such as humanitarian demining explosive ordinance risk education and others fall into which category does anyone want to pick up this question if I may just say very briefly there is a demining category which would capture some of these at least that would be a first part of the answer I'm not sure if Hannah or Jessica would have a better sense of whether the explosive ordinance risk reduction and so on would fall into any other category than that and I think this is correct these are included in the demining section so yes this is where I will look at and again for all of those you will have the three different levels of engagement and most of the so I'm not sure whether you can have that being encouraged so I don't think we should be encouraged to work on that more likely they will probably assist the government in doing that or maybe provide security to locations where this is taking place but that would be the category to look at right very I cannot see now yeah but it's there it's the demining option task okay so the next question is posed by Enric and he's asking the following does Pima also register UN Security Council support for each resolution for example which member state voted for against or abstained and maybe I'm going to answer this question because I touched upon Security Council decision-making at the beginning of the presentation so we look at mandated tasks we do not look at the voting record in this project and our reason for not doing so was because peacekeeping mandate negotiations in the post Cold War period were quite consensual and they are very rarely vetoed I can really think of only the example of the UN preventative deployment in Macedonia which was vetoed by China for reasons unrelated to the mission itself because Macedonia recognized Taiwan and China decided to veto that operation but in general the vast majority of peacekeeping resolutions are adopted by consensus and while we were talking I've quickly looked at the voting record for the past year and we do see some abstentions but we do not see negative votes on peacekeeping resolutions we had the rush up staying on the resolutions in the DRC the western Sahara and the support mission in Syria but I mean sometimes those abstentions are related not to the content of peacekeeping mandates but rather to the process of negotiations some countries would express disappointment that they weren't consulted enough or the process was too hasty so our reason for not looking at this is because we don't see much variation and then it's not always related to the content of peacekeeping mandates which is our primary interest okay then we have the question from Jenna do you attempt to categorize missions into types based on their mandated tasks for example observer or multi-dimensional can you briefly discuss the pros and cons of attempting to do this does anyone want to answer this question yeah I think I can give it a try so the benefit of our data is that we try to disaggregate these multi-dimensional mandates and missions into so what Xenia alluded to multi-dimensional mandates was a type of mission so after the 1990 when our data sets starts we actually in our data set we only see these multi-dimensional missions that include tasks that try to transform the political economic and social environment in the host country however now we could think of coming up with different types of broader categorization based on the mandated tasks that you find in our Pima data sets so what Xenia alluded to at the beginning the distinction between increasingly robust missions that are also mandated to use force targeting particular non-state actors in the country could be one marker of distinction from the earlier multi-dimensional mission so I think what we need to do here and what we can do based on our data is to think about maybe other broader categories of missions now can I get very briefly on on top of what Anna said I think and maybe related relates more to the pitfalls of I mean I think what would this data allow you to do is to really think more about what you mean with multi-dimensional for example so I think with the paper with Rob Blair and Hannah that I've mentioned before we have been thinking about that so we've been thinking about what multi-dimensional really means because sometimes it seems to be just about the number of tasks that are included in a mandate rather than the variety of tasks that peacekeepers have to do so the civilian component the peace building component and all these different things that are really ultimately even carried out by different types of personnel so I think when you when you have all these 39 different tasks it really pushes you more into thinking about what what's the best way not necessarily the best but what's the way that makes most sense to you to classify these operations oftentimes this depends on what you want to study what you want to research on and also with your observers right with your observers what do we mean with observers missions are those own missions that only have observers are as personal deployed so this is nothing to do with the mandate itself I mean it does have something to do with the mandate of course but you see it's just a different way of thinking about how we differentiate missions with each other from each other and so I think the good the good news is that the data allows you that flexibility to make the classification I think that it's and also makes you think a little bit more about the one that makes more sense to you great thanks thanks Hanan Jessica so the next question is about concepts of operations would you have any insight on the developments in the concepts of operations connobs over time I wonder if earlier missions with less mandated tasks still had similar implied tasks in the connobs I can probably try to answer this question and I guess that it's pretty much impossible to look at concepts of operations because they are internal documents and they're not publicly available and I actually wonder how systematic their archiving has been and for ongoing missions it would be impossible to get these documents from the yuan because they are related to the security of the operation and they're definitely covered by very stringent confidentiality procedures I mean maybe especially for some for some of the cold war missions concepts of operations were important documents but I think in the post-called war missions the mandates are quite specific and quite detailed and they usually define what peacekeeping missions do while concepts of operations they usually refer to how the force is deployed as opposed to what they do for example the regional distribution the type of bases that military peacekeepers work from so we haven't looked at the concepts of operations and I think that due to data availability it would be very difficult yeah may I add to this so I think this question is very good because it hints at another question namely how much of these mandates is actually implemented on the ground to which extent are these mandates dictating what peacekeepers are doing on the ground and this is the question that we are all interested in and that Jessica de Sarvatore and Rob Blair from Brown University and I tried to explore in this paper under what conditions do peacekeepers implement the mandated tasks and for this we have also coded what tasks are actually implemented by the peacekeepers on the ground so from from the tasks that you find in the mandate which ones are actually carried out and what what we see is that the share of the implemented task and from from the mandated tasks the share of the tasks that are actually implemented has not increased or decreased very very much over time and when controlling for levels of islands and mandate fragmentation so yeah maybe that that adds a little bit to to this questions question do earlier missions maybe carry out some tasks that are not written into the mandate that's that's something we cannot really answer but what we see is that earlier missions also quite closely try to follow what is written into their mandate except under conditions of violence or when the mandate is really complex and fragmented. Thanks Hannah so we also have a comment and then a question and the comment is thank you for your hard work reading all this UN Security Council resolutions well thank you for thanking us it was indeed a big investment of time and the question is do you expect any of your conclusions to change if you expanded this data set to the time before 1999 back to 1947 and beyond missions in Africa. If I if I think it's maybe something about that so if this relates to the results on civilian killings so on whether peacekeepers manage to protect civilians I'm not sure because we are relying on an analysis that just uses a more restricted sample so they're not using data that goes that back in time if that's what the question refers to however that refers on the other hand to the patterns in the mandated task the ones that magnets as illustrated I think we might see most parts mandates if we go back in time there would be my expectations but beyond Africa I think it may be it may be particularly interesting so if we think about again recent missions but beyond Africa I think it would be interesting to see if there's actually something going on in terms of a regional approach that UN tries to tries to have for these peacekeeping operations so whether of course keeping things constant as much as you can so thinking the levels of violence constant and other factors that are specific to the context where they intervene whether you do see still seem to be to identify a regional approach but this implies going beyond the sample that we have geographically so there will be I think my answer when it comes to going beyond the geographical scope for the temporal trends I think we will just see sparser operations so with fewer tasks mandated there will be my short answer thank you thank you Jessica so the next question is by Babu and the question is as follows do you look at cooperation with or support for national or third party forces we don't we do not call that information so we do not call from the some of the resolutions to include sometimes the requests for the mission to coordinate with other missions in the vision for example and this is not information that we call we specify in the in the code book which is the information we look for which is most of the times things that the missions have to do in relation to the government so we exclude things that I think by definition correct me if I'm missing it but I think this is one of the rules that we set in the in the in the things that we call so we remove this element of regional corporations or third parties we mostly call actions directed toward the government or that let's say directed towards states yes exactly there is a data collection effort by Lisa Hoffman and Corrine Barra on regional peacekeeping operations and their data set could easily be merged with the Pima data set in order to allow a first exploration of to which extend regional peacekeeping forces cooperate with UN peacekeeping forces okay great thanks now we have a few questions about protection of civilians so Walt is asking whether the strength of the warding for protection of civilians mandates is so he's wondering how it how it is measured because these mandates have evolved from being very timid initially and have progressively become much more robust over time in some context so Walt is wondering how the strength is measured and if you were to did you want to go ahead okay yeah so that's that's a that's a that's a great question so the first thing which is basically our coding scheme we do code where the mandate to protect civilians is something that emission has to assist the government in doing that or they have to do it that themselves regardless whether the government wants to work with them or not monitoring and encouragement so the other four category but it's sure that oftentimes the paragraphs where the UN mandates protection of civilians tends to be very long and details also include different references to other other I think there are other linguistic formulas that they use in those paragraphs that I think may allow you to look more into the strength beyond the engagement categories that we have identified for example the use of all necessary means that is something that by the way we code in Pima so we also have an additional variable which yeah you can see it in the first column use of force so that sometimes is mentioned in the same paragraph for protection of civilian is mandated and since in the road data we identified the paragraphs exactly where that task is mandated if you combine I think it's possible in principle to see for example what is how how let's say maybe not comprehensive but how many vulnerable populations is protection of civilian covering here sometimes it's a very general local population sometimes they refer to IDPs they refer to refugees they refer to humanitarian actors and I think if you if you if you use that information on the specific paragraphs and look at what other things are mentioned in relation to protection of civilians maybe that would allow you to go to get a little bit of that strength it's not necessarily the strength in the wording I think but I think it may highlight the relevance of that specific task for the UN for the Security Council sometimes they also mentioned that these tasks should be given immediate priority which is something we in fact we do not really code in the in the data but I think it makes it easier to go back to that specific paragraph and see if that type of language is used if you want to dig deeper into that but if you just want to use the raw data as it is I think the cross-references of the different tasks in the same paragraph would maybe allow you to capture some of that I would say yes just just to briefly add to this so we have a raw data version available where we have recorded the exact paragraph number so it would be easy easy to go to search through the column of civilian protection tiles and identify the paragraphs and the resolutions and then check whether these resolutions code civilian protection with priority or without civilian protection or comprehensively directed at different types of actors or more narrowly at some some more narrow category of actors and we have a question related to that so I would like to take it now Oisin is asking does the approach to modalities capture moments when the security council explicitly prioritizes tasks if not is there a risk that the granular nature of the data might miss the wood for the trees the true focus of the mission might be on a much smaller set of tasks than the list of mandated tasks implies I mean if I may start in terms of designating specific tasks as a priority it's also a very recent practice and it's maybe the last two or three years when a few missions have had some tasks designated as a priority but then sometimes they have a list of priorities and I think in the end they ended up having you know six seven main priorities covering pretty much all the tasks so I wonder how much additional information prioritization would have given us yeah that the recent hippo report from the UN has pleaded to have more prioritized and more sequence mandates due to this problem and what we read in the security council resolutions is that actually only civilian protection has recently become an immediate priority task but we do not really see also when we look at the patterns and trends in the data that this the scope of the mandate has been reduced and from the mandate language we also cannot really identify that there is any kind of implied sequence or implied priorities in these tasks but we think that is hopefully a trend where UN mission mandates will will be heading as we know like from anecdotal evidence it is difficult for mission staff to figure out what tasks if they have to pick and choose what tasks should be their priority. Okay thank you Hannah. We do have a few more questions on the protection of civilians. Given the breadth of POC issues how have you desegregated POC tasks? Does it cover the traditional POC tasks such as protection from harm or wider such as famine prevention access issues and protection from sexual exploitation and abuse and women peace and security? So if I can say a few words about that the useful thing I think was structured a codebook in a way that I think clarifies many of these or many many many points you might have on how the coding actually was done because we also identify instances that might sound like something that should have been coded but ultimately we do not code that so we try to be very explicit on what we called there and when it comes to POC we I think if this is a traditional POC task this is how we called that protection from harm and also because I think this more specific for example when it comes to sexual exploitation oftentimes this is referred in terms of due diligence within the mission and so as I mentioned before we do not code tasks that relates to other actors within the UN mission so if the mission is requested to make sure that peacekeepers do certain things in terms for example of their own behavior if they make sense that regulates their own behavior we do not code that information however if the mandate refers to and I'm referring into against to the SEA more generally sometimes the mandates refer to provide protection against sexual violence so here of course it's implied that that would occur would be perpetrated by non-peacekeepers actors that's information that we could but again we do not I think we do not have a category that codes things that the Security Council request the Secretary General to report on and that refers to what happens within the mission if that makes sense I it's in this case it's not necessarily within the mission because of course it involves interactions with civilians and with the local populations but when it's requested to monitor on certain things that the mission should be doing this is not a task that falls within our definition of task code that in a month in a dataset at least if that makes sense but any other reference to vulnerable relations that needs to be protected and they are for example in adp camps this is defined by a different category so it's the security the security provision for refugees for example so we have a separate set of I think of variables that could of mandated tasks that I think would speak to that not only traditional POC mandates if that makes sense yeah and I think human rights, children rights, sexual and gender-based violence as well as the securing categories of the securing modalities of engagement in humanitarian relief and refugees these are the wider civilian protection tasks and in civilian protection we try to stick to the mandate language as closely as possible and reduce arbitrary interpretation by ourselves and code this when it's the resolution actually states civilian protection. Thank you, thank you Hannah and Jessica and now we have two very interesting questions by Josh so the first question relates to the desegregation of tasks Pima codes 39 tasks but was the secretary general exaggerating when he said there can be 200 not 2 209 peacekeeping tasks is there a space for further desegregation? Yeah I think that then goes back to what a previous Tashin Oshin said about not seeing the forest due to the number of trees there's possibly further room for further desegregation especially since mandates will evolve right in the future and they will add other tasks so we have so many iterations in getting to those lists lists of 39 different tasks and we think these are the most sensical and especially if we want to reduce the scope of our own interpretation but we think like in the future it might be worthwhile to look at further desegregation for example in the use of forest or offensive operations if this is the direction that UN peacekeeping operations will go to or to look further into local reconciliation activities distinguished between with what type of actors the UN peacekeepers are mandated to do reconciliation activities local population or more traditional authorities and at what level I think there's some scope to some further desegregation but here again we can refer to our raw data set where we have also coded the paragraph numbers I think where it would be easy to seek out further into desegregation in one particular type of task. Thank you Hannah and Josh has also made a comment that in terms of further desegregation of protection of civilians tasks that some missions have been tasked with establishing and strengthening early warning systems that alert the mission to off threats to civilians and in our data set we do not code any language in which the Security Council might indicate how a peacekeeping mission might go about a specific task because sometimes the Security Council can be quite prescriptive they say you know missions should establish community alert networks they should engage with the local population establish trust but all those are means of implementing our protection of civilians mandated task and then Josh also has another question about active versus passive POC language is it possible that the mandate language is correlated with the capabilities of the mission or some other political factors for example rather than the mandate language influencing the government's decision to commit one-sided violence could account context to our government one-sided violence is occurring influence the council council's decision to include active POC language I think this is very likely this is very possible and it's also possible that maybe escalation of government balance of course just before I think Jessica is breaking up is Jessica back sorry can you hear me I think my connection okay I blacked out for a second it's possible yes the my connection is a stable a stable apologies if I something goes wrong again but I think this is very likely and it's also possible that the government will maybe escalate violence just before the mandate for active protecting civilians is authorized exactly because you know in advance that something is coming right so there are these escalation strategy escalation dynamics that have been picked up in the work that look at things that governments can foresee can anticipate because they know the UN is work because I mean these mandates are negotiated over some time they do not come out of the blue right so governments know that some negotiations might be going on they may be involved themselves in some of the tasks that needs to be authorized in the mandate which means that you know we that anticipates what's coming or maybe yes Jessica's connection is not very stable at the moment let's see if it becomes better or we can go to the next question and then see when jessica comes back whether she can finish her answer to the the other question yes yes this is a good suggestion hannah thank you so we have a question from digist and the question is about both women peace and security agenda and the protection of civilians so the comment is I think it will be interesting to see the increasing inclusion of the women peace and security agenda in mandates and see any linkages in implementation of mandates and the question about the poc could individual mission approaches also be a factor in poc mandate implementation as there are considerable number of missions mandated under chapter seven of the charter and yet are less inclined to use force thereby reducing physical protection tier of the poc mandate I'm happy to take this question but now jessica's back so maybe jessica can finish the answer to the former question uh it's not it was uh I think it was I hope the idea was was clear or did I I don't know what at which point the connection break down but broke down but I think just the last sentence or so uh yeah just the fact that government made them seven be part of those negotiations so they can definitely anticipate an ever most strategic behavior when it comes to how they want to use violence against civilians in particular I will I will stop there sorry yeah with regards to the question by tkist melka um I think this is a very these are two very interesting questions and they relate again to the peacekeeping as a conflict management tool and this is also a purpose for why we have created these data and I think it would be fruitful to merge our mandate data with another data set on what the peacekeepers do on the ground in order to evaluate to what extent a mandated sexual um violence and gender based violence tasks and also gender mainstreaming um tasks which are mandated are actually implemented on the ground and by merging um the pima data set was um these data I think you could evaluate um to what extent but also in which ways um the mission is actually implementing um the mandate a task and um the data comes with um this paper here by a player de sabatova and myself okay thanks hannah and um I think we've been very efficient and we have only one last question left in the q&a box does the increased specificity of mandates also correlate with higher strategic guidance and oversight by the UN headquarters or conversely with less freedom for um special representatives of the secretary general force commanders and police commissioners and I think it's a very very interesting question and indeed we have seen the expansion of peacekeeping mandates and in parallel the UN headquarters have produced guidance so now we have operational policy and guidelines on protection of civilians gender um civil affairs so we do see the production of more guidance and I guess the question about whether it influences strategic autonomy of senior peacekeeping leaders in the field is an empirical question um but my impressions from interviewing UN officials was that there is a degree of resentment against this long and wide and unmanageable peacekeeping mandates and very often senior officials senior leaders um try to figure out themselves what is the most appropriate approach to a peacekeeping mandate and one of my interviews had actually said like oh the christmas it was a christmas tree mandate with all the tinsel so various small tasks they would just see it as tinsel they would say like our core goal was electoral security we were securing the elections this is what we were doing and of course it would be nice to also promote human rights and interethnic reconciliation but I think senior leaders do take their own approaches to peacekeeping mandates yeah okay great I think this has been a fantastic presentation and I would like to thank you all for your attention for your questions we hope we have managed to answer all of them and our data set is publicly available I think there is a link in our presentation to a google site where the data is hosted so we encourage you to explore it we encourage you to use it we hope it will be helpful for a future research project on various aspects of peacekeeping diplomacy security civil wars um yeah Jessica so it's going to be posted on the website it's not yet there but we're going to post it it's the code book is there it's anonymous for business you can imagine but the data will be posted there as well okay yeah as soon as possible do we have like a timeline is it a matter of weeks or months or I think it's a matter maybe one week or so okay but in any case if you if whenever you check the data it's not available feel free to get in touch with either of us yes any of the four of us will be fine yes we were happy to email the data to you if you get in touch all right I would like to thank Hannah and Jessica and Magnus who had to live for this fantastic presentation and thank you all for your engagement for your questions it has really inspired us to think about some new avenues of research based on the peacekeeping mandates data yeah thank you for your interest thanks for the great question and thanks Xenia for moderating this yes thank you very much yeah I totally second Anna's comment yes please enjoy your afternoon and the recording of this presentation will be available online okay bye everyone bye everyone thank you


Hello, welcome to yet another session of our NPTEL on on linear and adaptive control. I am Shrikan Sukumar from Systems and Control IIT Bombay. We are well into the 10th week of our lectures on non-linear adaptive control. And we are now in the process of learning about not just design of adaptive loss for uncertain parameters, but also robust adaptive loss, which are not impacted because of disturbances that appear in the system due to unmodeled dynamics or external reasons that may impact the dynamical system such as what you see in the background. So what we were doing in this previous session is we had sort of started to look at the stability and adaptation design or update law design for this projection based adaptive controller. And the idea was that the framework was based on filtering the closed loop signals. So we actually filtered the known closed loop signals first and they were of course the important thing to remember was that these were all identical filters that is identical gains. And we then of course computed the dynamics in this filtered variables. This was another very critical step, right? And then we figured out that, you know, this dynamics has an additional exponential decay term which we ignore in standard stability analysis. This is pretty common. You can also keep it and continue your analysis, but then those terms are anyway going to go to zero. So it doesn't matter. We'll essentially we end up with a lot of exponential decay terms which you don't care about. So we don't carry it any further anyway. So we sort of ignore this. So we have a dynamics in the filtered variables which looks very much like the original system dynamics and this is what is rather key. And we choose a VF in terms of this, what we call a hat, which is in fact the projected version of. Yeah, so we actually have a phi hat plus delta hat here. And so this results in a hat always lying between a man and a max. And these are the bounds that are already given to us, right? These are bounds on the parameter that are given to us. And this a hat is what appears in the control of VF, right? And so therefore the controller remains bounded. And then we also, of course, had a short discussion and I mentioned that if the control law VF is the filtered control is bounded, then V is also bounded because VF dot is bounded and beta VF is bounded. All right. So this is again something rather important. This is what is the robustness aspect. And even in the presence of disturbance, we are not why nothing changes. All right. So then if we look at this, we started looking at the filtered closed loop. Of course, we had the EF dynamics written in terms of the new parameter error Z. Yeah, again, a new sort of expression instead of a tilde because we are using a non-surgeon to equivalence paradigm. Yeah. So we had an EF dot dynamics and we had a Z dot dynamics corresponding to the parameter error, if you will. All right. And the important step or the interesting thing to remember was that there were two terms, phi hat and delta hat, that had to be sort of defined. Yeah. And delta hat was just directly an expression, not a dynamical system. And it was motivated by the certainty equivalence adaptive law. And after that, phi hat is chosen just by computing a Z dot and cancelling terms that can be cancelled in the Z dot using a phi hat dot. So there was no Lyapunov analysis in order to compute a Z dot. So this is, again, another interesting perspective in non-surgeoned equivalence where your update law for phi hat is not computed using a Lyapunov function. All right. So once we have cancelled whatever we put, we get a nice Z dot law. All right. And then we sort of wanted to start the stability analysis. And in order to do so, we of course needed a candidate Lyapunov function, which has a rather interesting looking expression right here, not your usual Lyapunov function. The important thing to see is that this is non-negative. Right. And how we sort of claimed that was by trying to find a minima for this function. And since the EF and the Z terms are decoupled, we could deal with them separately. It's evident that this is anyway a non-negative term. In order to prove that this is a non-negative term, we took a partial with respect to Z. That is, we tried to find the minima and then equate it to zero. When we took a partial with respect to Z, the first thing we realized was that the partial looks very much like the Z dot expression, right? It contains a large piece of the Z dot expression. It's deliberately done, of course, because this will help us in the analysis subsequently. And so, essentially what we do is we took the partial with respect to Z. In order to find a minima or maxima, we equate this to zero. And so, it's evident that the minima is at Z equal to zero. Well, it's evident that the optima is at the Z equal to zero. And we claim that it's a minima. We leave it to the audience to figure out why it's a minima and not a maxima. And if we substitute Z equal to zero in this expression, we found that the second term goes to zero. So, what we are left with is a non-negative term. All right. So, that's sort of nice. That's sort of nice. Yeah. So, this is essentially what we are trying to say that this V is, you know, sort of has a nice lower bound. Yeah. Which is critical for us. Yeah. So, again, let me, so at Z, so this is again something I want to verify and stress on. So, at Z equal to zero, we have a minima. And that minima turns out to be lambda over two log cos hyperbolic of five star. And the expression for the cos hyperbolic is something like this. Right. The expression for cos hyperbolic is something like this. And you can see that essentially the cos hyperbolic is, so if we write the expression out, let's see. So, this is, I believe this will be lambda by two log of e to the power five star plus e to the power minus five star divided by two. Yeah. This is the expression. So, I'm wondering if this can turn out to be negative also. I'm wondering if this can turn out to be negative too. It may be possible, it's not impossible for this to be negative too. But the important thing to remember, so I don't want to say that this is necessarily, you know, I don't want to say this part that is necessarily positive semi definite. I believe this is certainly lower bounded. I believe this is certainly lower bounded. So, this is what I wanted to verify that you have tan hyperbolic z plus five star is equal to tan hyperbolic five star here. Yeah. So, this is what I wanted to verify for the minima and let's see if this becomes greater than equal to zero or not. So, this is what I wanted to verify a little bit more carefully today. So, so tan hyperbolic z plus five star is equal to tan hyperbolic five star. So, the tan hyperbolic function looks something like this. Yeah, it looks something like this. Now, the only time the two will match is I believe when z is exactly equal to zero. Yeah, I believe when z is exactly equal to zero. Exactly. So, that's the only time they will match. Only time they will match. So, when z is zero, this term is of course gone and then I have this term. I have this term which is going to give me lambda over two log posh five star. Right. Right. Log posh of five star. And that's what will be will give me a bound. Okay. So, this is what will be the expression. Okay. So, let's not worry about it's not exactly zero. It's not necessarily zero. Yeah. So, this is not necessarily zero, but this is essentially the lower bound that you will get. And this is essentially a constant lower bound that you will get. Okay. I don't think we have to worry too much about what that exact value is because for my Bob Lutz lemma type analysis, all I need is a lower bound. Okay. Great. So, this is where we this is where we were. So, I will start here on lecture 10.5. So, now all I do is take careful derivative. So, I take an EFEF dot which is this guy and then I take the derivative of this guy which is lambda by two partial with respect to z which is this times a z dot. Yeah. And now if you substitute z dot, z dot has exactly this term in the negative. Right. So, this is the mu XF squared. Right. So, that's what you get. You get the z dot term here. So, this, so this there is already a mu here. So, the z dot, so the z dot also contains a new here. Yeah. So, the new XF squared.  And this is also squared here. And there's a square here. Okay. I believe this square is on this whole term. And the square is on this whole term. This is fine. Okay. So, now you see I have nice negative terms. Yeah. Negative definite term minus KF squared minus KF squared. And I also have a square term here in XF times tan hyperbolic five star minus tan hyperbolic z plus five star. Right.  In fact, this whole term is omega. That's what we do here. Right. And so, you have minus KF squared minus lambda by two mu cap on a square. Right. And then this term can be written using our sum of squares as mu by two times EF squared with an R sum gain R. Yeah. I can use, you know, what I'm using here is that AB is less than equal to, well, I'm actually doing this.  So, this is less than equal to half R A squared plus B squared by R. Yeah. That's what is being used here. If you notice from here, so the mu remains as it is. And from these two terms, I get R EF squared plus one by R omega squared. Right.  So, you get this term. Right. And therefore, you get V dot negative semi definite if lambda is greater than two over R. Right. And of course, K greater than mu times R. Now, one might ask why did we, one of the important questions to ask is why did we need the lambda? Right. Why did we choose put the lambda here? Remember one thing. Okay. Even though we get this nice term, this is not a negative definite V dot. Okay. Remember, right? Because V was a function of EF and Z. And it's not very clear that this term is negative definite in Z. Okay. Because there is an XF also. Right. So, negative definite with respect to Z is not very clear here. So, this is at best negative semi definite only. Now, because it's negative semi definite and I would like this to sort of dominate some other term. Yeah. So, I have to make sure that this term is smaller than this term. Right. And so, I take an arbitrary lambda. I don't know the value of lambda. Right. I took some lambda positive. Anyway, this lambda does not enter anywhere in the control law. So, it's not like we need to know the value of lambda is just for the purpose of analysis. So, this lambda now has a 1 by r. Right. So, I can choose r large. I choose r to be big.  And correspondingly, I have, you know, I have this r here. So, no k can be large. You know, if I choose a large enough k, I'm done. Okay. So, that's so, if r is small, sorry, if r is large, then k is large. Yeah. And lambda needs to be small. Okay. Vice versa.  You can choose any k, arbitrary k. Okay. Then r has to be really small. So, if r is really small, then any k will work. And you choose any k correspondingly, there is a small enough r for which this will be positive. Right. And once this is positive, this becomes very large. So, then lambda has to be very large. Right. But we don't care. This lambda doesn't appear in the control law. Right. So, lambda being large doesn't change anything for us. It's just for the purpose of analysis. So, this is a rather neat trick. Yeah. In analysis, when you don't know how big this gain is, you know, and you don't want to push the control gain k large because k actually appears in the control law. Right. So, k is, I mean, k is not here in, in, you know, in vf. Right. k is not in vf. But if you remember, k is there in the control law. Right. Because we have to implement a u and v contains k. Right. So, k being arbitrary large is not a good idea. Right. So, if you choose any small positive k, there is always, one can always say that there exists an r such that k minus mu r is positive. And if the r is small, then all you need to do is have a large lambda in the analysis. But again, it's just for the analysis. So, it doesn't change anything for us. So, we are more than happy. All right. Excellent. So, that is the purpose. So, what we have now is we have a v dot, which is v of course, which is lower bounded. And we have a v dot which contains these two quadratic terms. So, it should be sort of obvious to you for all of those who have done bubble at Slemane signal chasing analysis several times that, you know, you can prove that if and omega go to 0 st goes to infinity. So, this is something you can always prove from this kind of a Lyapunov like analysis. All right. We are not claiming that v is positive definite and lower bounded at 0 and all that. But we know it has a lower bound. It is non-increasing. Yeah. So, we can prove all the quadratic terms that appear here are going to go to 0 using bubble at Slemane signal chasing. And that's what we do. Like right here. We can also show that E f dot goes to 0. Not difficult. We have done this before too. Once you prove E f goes to 0, we can prove E f dot goes to 0. And if E f dot and E f both go to 0, what do we know? We know from our filter construction that you have E f dot equals minus beta E f plus E, which implies E is E f dot plus beta E f. Yeah. So, if both E f and beta E f dot go to 0 means E goes to 0. I know that's what we have. Yeah. So, the other additional thing we sort of get, which we don't get in certainty equivalence. Remember, we never get a term in parameter error in certainty equivalence. Right? But here we do have a term in parameter error. It's a very non-linear term. So, not very obvious what this term means or what it looks like physically. But we at least have some kind of a term which goes to 0. Right? We know that this guy goes to 0. And this is sort of an attractive set for the parameter error. The important thing to remember is that if you start with 0 parameter error, that is when z is 0, suppose z is 0, then this quantity is 0. So, omega is 0. If you start with 0 parameter error, you will stay with 0 parameter error. Because look at this. I mean, in the absence of disturbance and errors, et cetera. First, if you look at this term, this is 0. This is 0. z equal to 0 is an equilibrium. Right? So, therefore, this right-hand side becomes 0. Now, this is not true in certainty equivalence. In certainty equivalence, this would have been your update law. See, even if you started with a tilde as 0, the right-hand side has no a tilde in it. So, it does not matter if you started with a 0 a tilde, you will still change the parameter value, which is of course, seems unhealthy. But well, that is the sort of solutions we have. In this setup, if you started with 0 parameter error, in this case z being 0, then the right-hand side is 0 and you do not move from it. Okay? So, it sort of creates an attractive set. In fact, attractive and invariant set. Okay? Creates an attractive and invariant set. Right? So, if you stay in that set, you will remain, if you start in that set, attractive plus invariant set for the parameter error. So, if you start in this set, you will remain in this set and you will be attracted towards the set also. Okay? So, this is a rather interesting property. Yeah? Which actually improves the adaptation behavior for the system. All right? Excellent. So, I hope that was clear and you understand that. Now, of course, we didn't go into any further details now. Right? So, but remember that in order to compute the actual control law, you have to compute v, which is equal to vf dot plus beta vf. Right? And we already have shown that vf is going to be bounded. Right? vf is going to be bounded because all closed loop signals are bounded. Right? And if vf is bounded, then vf dot is also going to be bounded. I mean, that also can be proven. We are not proving it. So, I will actually say prove boundedness. Yeah? I would leave it to you as an exercise to prove boundedness of this. Once you have the boundedness for vf dot and vf also, then you know that v is going to remain bounded and so is you. Yeah? And this is not going to be affected in the presence of disturbance. Again, we have not done any analysis with disturbance notice. There is no disturbance analysis here, but what is happening here is the fact that the parameter, the design is not going to change in the presence of disturbance. Right? Only the Lyapunov analysis changes. So, basically you will start getting some terms corresponding to the disturbance here. That is what will happen. Right? This will happen. Right?  So, all these steps remain the same, but then I will have something like this. But the good thing is, because I have negative definite terms in both Ef and omega, so nothing changes really. I will still get like a residual set in the Ef, which will of course move to a residual set in the original states and all that mess. Yeah? And of course, my parameters remain bounded, so my control remains bounded. My control will never become unbounded. It's irrelevant what happens. Yeah? The control is never going to become unbounded. Neither is the parameter estimate. Yeah? So, the disturbance may affect how the residual set, I mean, sort of going to zero errors. Right? So, you know, instead of going to zero errors, you may not go to zero errors, but it doesn't really, I mean, you will get a residual set as you expect, but you don't change anything in your parameter boundedness nor in your control boundedness. All right? So, that is the sort of important thing to remember. Okay? So, this is the projection method. By the way, this is only one kind of projection method that I have specified. There are other ways to do parameter projection. In fact, this is a rather unusual way. The more common way is using the notion of convex sets, which I am not presenting right here, but it is available in, you know, I mean, in results from year-on-year and so forth. Yeah? So, you have references which talk about your convex sets and how to do projection on convex sets. Yeah? I'm not going to, I'm not going into that right now because, you know, for the sake of time, we have to restrict our material. Yeah? But this is a pretty solid, pretty good way of doing parameter projection. Yeah? And parameter projection as you can see is critical in adaptive control. Okay? Now, one of the concerns that some of you might have is that projection requires knowledge of your bounds on the parameter. Without parameter bounds, there is no way you can do projection. And if you remember, in the beginning of adaptive control, you did not assume any kind of bounds on the parameter. Right? So, what happens if you don't have parameter bounds available to you and you still want to impart robustness to the adaptive control? Right? So, these were, so this discussion began, of course, when we had that, you know, the fighter jet crash, right? And results came about in a few years after that. And the first one of them was first, whatever, first seminal result was by Ionu and Koko Tovich in 1983. And this is called, this was called a sigma modification in adaptive control. So, I will sort of classify this as in the absence of parameter bounds. Okay? In the absence of parameter bounds. So, the question is, what happens if you don't have parameter bounds and you still want to impart some kind of robustness to your adaptive control? Right? So, we start as usual with the same system. And this is called a sigma modification in adaptive control by Ionu and Koko Tovich. We start with the same system, x dot is Ax plus u plus g. And we know that there is a bound on the disturbance, right? I mean, we don't know the value of the disturbance at each instant in time. But of course, we do have knowledge of a bound, very reasonable assumption, right? If anything, you can just keep a very large bound, just to be conservative. But we do know a bound on most disturbances, right? For example, if I'm flying a drone, I have a pretty fair idea of how much the wind velocities will be. I mean, I have a pretty good idea of the range, right? Of what the wind velocities would be. If I'm, again, if I'm flying a satellite and, you know, I have actuator issues, I don't know how well the actuators perform if they precisely produce the amount of torque that I expect them to. I may not know the exact values, but I will still know how far off they can. So, that's essentially what's the job of a good engineer, right? You have a pretty good range in which your system will operate. So, what is the objective? The objective is, as usual, to try to drive the error between X and sum bounded to actually X m to 0, right? So, as usual, what do we do? We create the error dynamics and we have this certainty-equivalence adaptation law. So, we are back to the certainty-equivalence adaptation law. So, the idea is, when you do a, you know, if you do a certainty-equivalence adaptation law, you will take a v, which is something like 1 half e squared plus 1 over 2 gamma a tilde squared, pretty standard, where a tilde is a minus a hat. And if you do the v dot and compute everything and try to find the a hat dot, you will see that a hat dot is gamma times e times X, where gamma positive is the adaptation gain, all right? So, what Ianu and Kokotovic proposed was the sigma modification, which meant that you added damping sigma a hat term, so this adaptive law, right? So, the whole problem was that the a hat dot update law never contained a term in a hat or a tilde. Of course, it can't contain a term in a tilde because that's not implementable. So, Ianu and Kokotovic did the next best thing. They added a nice negative term in a hat, all right? And then, of course, we did some analysis to show what happens. And this analysis is what we will see in the subsequent session, all right? Excellent. So, what we looked at today is the sort of completion of two of our parameter projection-based adaptive control law. We had rather interesting Lyapunov candidate and we took its derivative. We also had a sort of lambda coefficient on this Lyapunov candidate, which we saw was very useful for analysis and played no role in the control. So, it did not matter how large we took it. And we also realized that this non-certainty equivalence type paradigm in projection gave us a sort of attractive and invariant set, which has nice properties such as if you start with zero parameter error, you will remain at zero parameter error in the absence of disturbance. So, these were the kind of properties that were absent in the certainty equivalence adaptive function, right? And finally, we sort of started to look at the signal modification in adaptive control, which would be a way of imparting robustness if you did not have the knowledge of upper and lower bounds of your parameter. Excellent. So, we will continue with our discussion on sigma modifications in the subsequent session. So, I invite you to attend. Thank you.


Hi, I'm Mary Keena, Livestock Environmental Management Extension Specialist with NDSU. I'm here at the Carrington Research Extension Center where we're preparing the compost rows for upcoming August 4th online composting workshop that we're doing in conjunction with the University of Minnesota Extension. We're very excited to tell you that we're going to have an online workshop this year where you can join us to learn everything about site selection, maintaining a compost row, the economics of compost, as well as talk to online, talk to live producers who do this in real life. These compost producers are going to join us for an online discussion that you're invited to on August 11th. So on August 4th we'll have all the content up. On August 11th you'll join us for an online live discussion. We sure hope you can join us and we want to thank the North Central Region Center for sponsoring this program.