We'll call the meeting to order and I think on the agenda what we wanted to do was move the agenda items to the next meeting. So the first part would be tabling our current agenda for 710 to the 724 meeting. Except for the tax rate. You have to set the tax rate tonight because I need to print tax bills tomorrow. OK, except for the tax rate. Sorry, I would move to table all agenda items except for the tax rate to the July 26th meeting and amend it to discussions about the current and ongoing flood. Yep. So we have a second. I can't hang out. I got it on my phone. I can't see it. So moves. So Dave's good. OK, so there's three of us. So we're good. All right. So let's let's just do the tax rate piece first. OK. And then we'll move on to the. The emergency flooding discussions. OK, so the tax rate in your packet, I gave you all the information. I gave you the state tax rate, the amended equalization study, as well as a copy of the updated 411, which is that what is the basically a summary of the brand list. So the amount to be raised for taxes was two million four hundred two thousand six eleven, which is everything that passed at town meeting. And then, including all the additional, the library, the skate park, the playhouse, the local agreement rate is the amount of school tax that we pay on the voted, like at some point in the past, you voted to give veterans a thirty thousand dollar reduction in their property value. And we also vote every five years to give the Grange make them tax exempt. So what happens is the law requires that we pay the school tax portion of those things. So that comes up to the seven thousand six hundred seventy six dollars and thirty five cents. That's what your local agreement rate is. So and of course, the school tax is set by the state, so we have nothing to do with that. So it's pretty easy. You take the grand list and, you know, divide it out with what you need to raise by taxes. And there's the tax rate. So it is eleven point five percent over last year. The local agreement rate is down a little bit because one veteran sold their house and another veteran did not apply for the exemption, which all goes through the state. And then the homestead tax rate is up point six four. So the overall that's mean the homestead tax rate is up five point one five percent. And the non residential tax rate is up seven point three two percent. So that the it's so that's it. Do you just need a motion that states tax rate will be? Well, sure. I mean, does anyone have any questions on the tax rate or the math or how we got there? Otherwise, just a motion to approve is fine. Move to approve the twenty twenty three twenty twenty four tax rate. OK, second. Jean's giving you the thumbs up. OK, all in favor. I I OK. All right. We're good on that. Thank you. Thanks, Dave. So let's let's dive into the. Emergency situations going on in Bethel. Well, Trace, why don't you just take us through what you and your team have been doing up until now and then after maybe kind of explain to us what the next steps will be, you know, tomorrow morning or the next day or two or. Type deal. OK. So I got to Ben fall about 10 o'clock yesterday morning and started doing, you know, additional emergency preparedness things. Obviously, people we like to think watch the news and keep track of the weather and that it wasn't a big surprise. But we I started making, you know, information for obviously from Port Morum Facebook, our website. We had had a small event on Friday where we received three inches within 15 minutes did some significant damage, really localized. Interesting because Camp Brooke didn't get any rain, but yet North Road got hammered. So, you know, so we already had a mini event on on Friday. On Saturday, the state of Vermont, as well as two rivers, came to Bethel to document because if these become FEMA, which I assume they will, they would be documented as separate events. So if you've had damage Friday, but then you had more damage today, those are separate events, so they came to document those.  If you haven't been paying attention, there's there's flood coming. So you do that through Facebook, from Porch Forum, the website. We had an outgoing message on our office phone that said you can call 211 if you needed a place to stay. You could call 511 for road conditions. You know, and we knew at that point that we were going to open at least the town hall for a shelter. So we did that. So I talked to the emergency shelter team, so we made those plans. I talked to the state emergency watch officer and he was scary because he said trees, they're thrown around things like tropical storm Irene and he's like, it's going to be bad. And I'm like, OK, so last night at, hang on a second, last night, thank you, at 6 30. We had a meeting at the fire station to again get prepared, make sure that everybody chain saws were sharpened. Everybody had fuel. Morgan had met, you know, talk to the road crew. We made sure that we had all of our cones that we had signage and all the stuff that you need to do to be prepared. Then I stayed in Bethel last night. And then this morning about 3 15, Morgan was out. You, Morgan was out checking roads. I was at the town office at 5 a.m. and we started. I just created spreadsheets and we knew that we were going to have two employees that couldn't come because their homes were being evacuated. And we just started keeping a list of letting you know what's going on where and then Lindley graciously came in and worked the office with us for most of the day to answer phones. And we have just lists of all the roads we kept track of the time. People called who called what they reported, dispatch the road crew as needed. I personally dispatched the fire department to evacuate upper Gilead by him and a portion of Gilead Road. First thing this morning, I think I dispatched them around 7 a.m. I dispatched them again later to evacuate or start evacuating River Street and Ram Street. And just to be clear, when we evacuate, we ask you to leave and we tell you what's going on. If you refuse, that is your right. We may just not be able to come back and get you because we can't risk life and limb to do that. So we have just been at it all day. Taking calls and now I'm hoping that the road crew has gone home. As I said, Morgan has been out since 3 a.m. And the guys since five get some sleep. The fire department is out. So if anyone has an emergency, they'll call 911. I would say that the majority of all roads in Bethel are currently closed. So I'm not sure what more we have left to do because the volume of water just the roads then the ground was already saturated. So it was just bringing with it material trees and it was too much water. The culverts just weren't going to take it all at once. So now what happens is hopefully. Fingers crossed that the rain is stops around eight or eight thirty tonight. There's going to be what we call a bubble because all the water that has come, you know, up above in the mountains is coming down. We're going to see where we get. We may have to re evacuate the trailer park because they had gone home because the water had receded once we got a state culvert open. But it's going to depend on, you know, that bubble. And the last I saw is overnight there was precipitation but very little bit and maybe a little bit in the morning and then drying out. So I talked to Morgan, the road foreman just before this call. He and the guys are going to come out at six a.m. And they're going to start, you know, doing roads again and maybe around eight or nine. He's going to come to the office and we're going to regroup and it's all going to be about triage. Who has the most people on what road is how it's going to get fixed? Probably by then I will have spoken with our VTrans representative as well as two rivers. And we haven't heard from FEMA yet, but my guess is we will. And as Chris can attest, there is a ton of paperwork that goes with that. So we have been drilling that in everybody's head in advance, saying document, document, document. And that was part of our pre-meeting last night. And so I will take my spreadsheet, Lindley's spreadsheet, Kelly's spreadsheet and kind of put them together tomorrow to see, you know, who's called in and then we're going to make a plan. And obviously some of it will be done by the road crew. There may be some contractor stuff. Luckily we had already purchased our gravel from a lot from Pike and they had already been delivering. And I think they may have been delivered some today as long as they could get through until 107 was closed. So at this point, for lack of a better phrase, we're waiting for the dust to settle, right? And the rain to stop. So we can get a true picture. It looks like it's going to be dry tomorrow afternoon, dry Wednesday and of course more rain Thursday and Friday but I don't know how much. So hopefully no one loses their home. And people are able to go back to their homes in the morning. Last I knew we had 12 people at the shelter then some people left and some people came back. So I'm not sure exactly the number of people we have at the shelter currently, but Denise, God bless her and Joanne Marshall, they are spending the night at the shelter, at the emergency shelter at the school. So it will remain manned overnight. So which is great, so thank you for that. So that's what I know. And I, Terese, I would just suggest having, well, kind of being through that spring flood there event that we had in 2019. Yeah. Because FEMA is a lot of work. So what I would suggest is that we break up our town into different quadrants. Like we did then. Yeah. And in each quadrant would have its own set of numbers. Yeah. And then just remember it sounds crazy, but we have to have pictures of everything before we fix anything. Well, what I did last night, Chris, at the fire department meeting and then again with the road crew and I had people that did not have an Apple that could take a GPS with their phone. I had them download the app, the solo locator. So it automatically GPSs because I remembered that you and I and Mo and Judy were out trying to find GPSs for the photos. So I have asked. So that was pretty clear along with documentation about if anybody, the fire department or the road crew went to a call, it was who was there? How long you were there? What road you're on? What tools you use? Because even if they're using a hand shovel, there's a FEMA rate for that.  Yeah. And if I remember right, the first 24 hours they'll allow kind of a lump sum of, they call it emergency period where you could just kind of lump together your costs during that period. Yeah, they'll let us put it back to preconditions. I think we can upgrade culverts by one size during that, which they didn't use to allow us, but basically you can't put it back better other than an upsized culvert. You can't rebuild that, you know what I mean? It has to be as well. Well, I think that's what it was for. During what they call the emergency period, I'll make it up. If you're gonna bring two truckloads of gravel just to get somebody out of their home, you can just lay it down as a blank check type thing. Yeah, exactly. But after that, once you start doing permanent fixes, they all have to be numbered according, you know, if you have located pictures in the whole nine years. So. Yeah, know that I know, we have to bid it all out because I did all the bids for 2019, but it was just after, but no. And I think too, once I pinpoint a meeting I'll see, you know, what your availability is. I also want to see about Chris Bump and two rivers in the state because they will also help us with documentation and laying out the work. Cause some of it's gonna be contracts or some of it's not. I will say, last I knew our temporary Pinello bridge was also hanging on by a thread. So we'll see what happens there. But yeah, so no, I will definitely be requesting help from the state of Vermont, two rivers, FEMA, whoever to help us organize our you know, the work stuff. And remember too, Camp Brook Road is a federal highway. So they'll come in and we'll get that redone and are fixed however. And that's a hundred percent covered because it's a federal highway. So we won't have to pay out of pocket for Camp Brook, but we will be on the hook for our ERAP, which is 12 and a half percent of whatever we spend with fixed stuff. So. And how are we doing right now? Yes, Dave, we can. I took half an hour, but I think I got it fixed. Good job. And how are we doing in regards to like supplies for the emergency shelter and things like that? I think that she's all right. The food shelf had gone and donated food. I think Denise was making them spaghetti dinner and salad for, so they were okay. I talked to the state of Vermont before I came home this evening and they are basically requesting that we stay open overnight because at this point the only place we could ship people to would be Barrie or maybe some place in Randolph, but they didn't really want people on the roads. And, but by tomorrow hopefully people will be able to go home if they can't go home because their home has been lost, then Red Cross usually will come in and work with them to find them living quarters or they'll go to a friend's house. So. You can't get into Barrie very well right now. We have some people from the park that came back. Some are refusing to come back for whatever reason, but there's about 10 or 12 people here now. I was, thank you Owen for taking me because I was starting to get the spaghetti thing ready and I was like, are you going to the meeting tonight? I'm like. So anyway, yeah, we're getting spaghetti. I've got stuff from the food shelf. I have the key. I can get more stuff. I've got milk and cereal for breakfast tomorrow, yogurts, bananas. So we should, and I have, I bought some bread and we have separate peanut butter and jelly sandwiches or toast. So we're going to be pretty much set up here tonight. And Cindy has people coming in tomorrow morning around eight o'clock to take over for us. Great. That's good. So the other thing I forgot kind of came to me when Denise was speaking is, so I don't know what state the pool is in. Obviously if the pool was going to overflow, it was going into the parking lot. It wasn't one of my major concerns.  They can hold about eight hours worth. I think that Richard had already, I think when I was leaving town, I saw a truck coming and they will, he was going to have to have a couple of things pumped out, but Bethel Mills pump station was going to be under water. So that's why we shut that one down, obviously. And so we're holding right now. If he had to have it pumped, then that's fine. It just means it didn't go all the way through the system, but we have it trucked out. The water system is currently operational, despite that we're at one reservoir because of maintenance. Worst case scenario, we lose power on Peavine Boulevard, then we have water for about a day and a half. And in the reservoir, we had put out a notice today asking people to slow down their water and sewage usage. Don't flush the toilet all the time. And so just a kind of because of the heavy rain that comes into the system and it increases our load. So. There was a pump truck across the street from the pool. Yeah, maybe. Oh, they pumped out over there. Yeah, that's yeah.  But hopefully that the rain stops and it recedes and we, you know, the Bethel Mills pump station has been through Irene. Tim redesigned it after Irene. So hopefully, you know, fingers crossed. So I think that covers every aspect of the town, Chris, as far as. Will roll trees. Yeah. My grandson will tell you if it's yellow, let it mellow. If it's brown, flush it down. Yes, I've heard that one. So yeah. So anyways, that's where we're at with that. So thank you, Denise, for the shelter update. Okay. A question that I have. Well, two comments. One is I called in later this afternoon when I saw water under the railroad bridge at Finley Bridge. And that meant that there was really no access from Randolph getting into Bethel or no Bethel getting out of to Randolph. There was no way to go north. Because that's because and I You, we lost you. Just wanted to be sure you knew that. Okay, yeah, we knew. Yep, because also route 12 by camper corners was flooded. There was actually people were driving through up to like three feet of water. So yeah, at some points there was there, but that was later in the day. There was access to get out of Bethel. But yes, and actually when I got out of town, I was going to get the interstate to leave Bethel. And if I hadn't left what I left, I'm not sure I could have got out because 107 was flooding right there by after Ellis music, there's the church right there. I can't think of its name. I apologize. So it was flooding right there. So we were all like shimmied over in the breakdown lane taking turns to get through. We had no trouble getting down to Hanover and we're staying here tonight because I have a procedure in the morning. They don't seem to have as much rain and water as we do, but that may be because we're not seeing it. We're downtown, but they're anticipating their rivers and they're requesting it 2am this morning. Yeah, tomorrow morning. Yeah, everybody's different. So who knows? Yeah. Terese, what time did you say that you were going to meet down at the office tomorrow with? I'm not sure. I just, when I got home Morgan, I told them eight or nine. So I would just message him when I got into town, I was going to let you know, because I'm hoping it won't be right at eight. My guess is it'll be nine because if they come on at six, they need some time to check some roads obviously. And I need to figure out if two rivers or Chris Bump or someone's coming from the state, but I'll let you know. So we could be there. But yeah, I have my map out and I figured we'd do the same thing as April 2019 and break it into quadrants. And but this time, I'm not sure who's going to help with estimates because last time that was a problem, the estimates weren't good. So for the road work, so. Yeah, I can, I'll put that up tomorrow. Yeah, I'll catch up with you whatever time you want to meet this message. All right, yeah, I will. We can start putting that together. Yeah, and I mean, we have a lot of the documents from April 2019. And you know, some, I have all the RFPs and whatnot. And frankly, unfortunately, some of the roads are the same. So. Right. But we'll see what we're going to do tomorrow in an emergency. I'm sure that I'll have all sorts of instruction. The state and theme are going to let us know what we got to do. I have all the spreadsheets from the projects that we did before. So large projects, like you say, we can keep going. And I can't remember if it was 72 hours or how much, but once the rain stops, we will get boots on the ground. And that was the other thing. I did have three contractors strategically in three, in different places in town before the storm just in case as well. So we did have some pre-placed equipment. So just put out to you that I'm working from, I mean, in town this weekend working for myself. So I have flexibility if we need extra hands or I know like during, in 2019, I was used as a flagger, you know, things like that. So you. Okay. Yeah. Thank you. I'll let you know because I don't know, honestly, with two employees who hopefully do not lose their homes tonight. I just don't know the situation. So yeah, but thank you. We were a wonderful help today. Because as a boy today, Kelly, I said to Kelly, we got to call Lindley because we can't, the two of us can't do this. The phone is ringing too much. My cell phones ringing. I'm like, we two of us can't handle this. So it was great. So thank you so much. And Lylee brought me food. So that was wonderful. Therese, I'll be home. Jean and I will both be home in the afternoon. Okay. Soon after noon. So if I can help with any of the office stuff, please let me know. Okay. Thank you. Chris, it looks like Lindley has his hand up. Thank you. Leonard has his hand up. No, I just wanted to say thank you so much, Therese. Thank you to sit back board and especially the road crew. Maybe you had the mini event on Friday. They came out on Saturday about two hours after I called and they fixed the call, but they made it open and they put some heart pack downs that we could use to road. Of course, everything today was washed away after it again. But of course that's why. I was really impressed by that and I want to say thank you. Well, I saw your front porch forum post and I copied and pasted it and sent it to Morgan because truth be told, Thomas, we get a lot of complaints but it's rare that someone takes the time to send a compliment. And it really meant a lot to Morgan and he always shares those with his guys. So thank you for taking a minute. That was it. I tried to tip the guys but they didn't want to take the money. I have a question for you, Teres. I know there's some restrictions with FEMA and the funds you get to reimburse and to fix things but it seems like these storms are teaching us that some of the culverts are just too small. Absolutely. Is there no way to petition that so that we can make changes? Do they have any formats for that so that we can actually make changes to those? Sure. Yeah, because we did do, we have this whole wonderful, actually it's cool, this whole binder about all the culverts and we replace them and when we replace a culvert we automatically upsize. That's usually, that's just the plan and any grant that we get to do road work we upsize the culverts. What FEMA used to do was if you had a 15 inch, you only got a 15 inch. Now they have saw the error of their ways. So if FEMA say you have a 15 inch and we come in we're gonna put in an 18 inch and it's hard too because you're sizing for 500 year storms sometimes. So for us to take your culvert and say, okay, we're gonna go from 15 to 24 maybe just be unreasonable but we do always size up and when we look for projects we have this big binder and Two Rivers did a whole inventory of all of our roads and culverts and that's how we get a lot of our grant money Leonard. They, we pick what they're called is hydrologically connected segments and if you're near a river so sediment and things are running off those are priority and we have this whole book of medium high priority and I have a grant right now that has to be done by the end of September and that's gonna be on Macintosh. So sometimes what we do is we look at that and do a high priority. So if old route 12 was on there but it's a low priority and we only get one of these grants a year you know how it rolls. Yeah. I just find it strange that like up top here we have this large culvert and at the bottom funneling into that we have a smaller culvert. I just find that strange. It could be who knows what happened originally, right? If you had a bridge there that went I don't know the whole history but probably it's not uncommon in this town. Up there on our hill we have a four foot culvert that dumps into a three foot culvert. Yeah. Washed out three times in the last 10 years. Yeah. Put back a three foot culvert. So yeah. It's just okay. We gotta look at that. Yeah. When Irene happens, we asked the crew that was here was not a Bethel crew. It was I think a FEMA crew. Uh-huh. Said like can't you, it's open. Just put a new bigger culvert in it and said no we can do that and it just dumped dirt on it and that was that. Yeah. Yeah. Yeah. Yeah. It is. It's funny and some of it is we just don't know why it was what it was. And a lot of times when you put in a culvert it lasts a long time. So it's just kind of the way it goes. But there is, when we are replacing them there's a method to the madness. Why they are the way they are now. I have no. My dear. Yeah. No. Thank you. You're guessing as good as mine. Yeah. Are we allowed to pour concrete head walls? The town of Bethel? Yeah. It depends, Dave. Yes, we can. Sometimes the head wall that gives out. Yes, we can. Yeah, it depends on the job. If it are with the project, I guess I couldn't say as a blanket statement. It depends how big the culvert is, whether or not I need to get permission from A&R for Jaren Bork or that sort of thing. But yes, we can. Sometimes we put in our own or we'll use stone. It just depends on the situation. But usually a lot of times we use precast, right? Chris, isn't that what we used up on? Where the? Didn't we do one up on Christian Hill? And I think we used a precast, Dave. Most, I mean, most of the culvert issues are due to debris and I think culverts are tricky.  So you do a speed study and you find out that traffic goes faster so that they won't allow you to lower the speed. And it's kind of the same thing with the culverts is the engineers have to get out there and approve the size of the culvert they put in. And most of the time what damages the culvert is the is the debris that comes from down, you know, tree debris, rocks, that kind of stuff. So. But, you know, I looked at pictures of that culvert out on the Bevine Road out towards the old cross and the fish hatchery and I'll bet, because I know I saw what that looked like and that didn't have much of a head wall on it. And it might've started when the culvert started to get full to seep around and once it starts seeping around that head wall, you're done. Yeah. And I know. I mean, we don't, I mean, and that's a trick that in Vermont, like none of our roads in Vermont are built for any type of a large flood event. None of them are. I mean, you would need culverts the size that you drive trucks through, you know, and it'll probably never happen. And that's kind of a challenge with it is, but FEMA does allow us to build back and in a lot of cases, build back better. Like in the 19 flood, we were able to, you know, install either rock, swales where we didn't have them before and a couple of cases, we put some culverts in that made sense that we have before.  I know. It is frustrating. You know, I will say that from a bit, been out and about all day, you know, I don't think you're ever 100% ready for any type of event, but I think that everybody involved today seems to have a plan and there's a lot of good coordination going on out there. You know, a lot of it's kind of, your hands are tied. You kind of got to wait for the storm to pass. Seems like everybody, the coordination was pretty good on, you know, when to close things, getting some of the mobile equipment in early. A few culverts were able to unplug early this morning that could have led to bigger issues if we hadn't done that. So that was good, which I think, you know, like the one up here with Derek, Altigarie did, you know, probably save the trailer park and then obviously the road spill, the water spills over across the street into those houses on the east side of Route 12. So I think, you know, I think there's some cases that we've been more proactive this time that has saved, it's hard to say, but has saved other potential issues that we could have had, bigger ones. I would say, I didn't want to say this, but you know, it definitely is very, very similar to Irene type weather today, other than it took longer for the rain to hit, which I think in some cases gave us more time to react to the storm, which was nice. But yeah, everybody's been doing a great job. I definitely would make sure that everybody gets plenty of rest tonight because it's going to be, you know, a long couple of days, you know, two or three days just to get everybody mobile again, right? I mean, people so they can get out of their houses and then we'll work on the long term fixes. So. Exactly. To sort of second what Chris said, I do agree that we were far more prepared. And I think so much of that is a testament to Therese and Therese being ahead of things and, you know, getting the crews in all the different areas ready and on standby. And so thank you. That's huge. Well, thanks. Some of it too was just, you know, timing people really that have been here through Irene before have been really helpful just saying, okay, Therese, this is what happened before. And then of course getting it, you know, handled or at least some of, sorry, but at least it didn't come all at once. That was really the issue with Irene and we just couldn't, you couldn't have done anything different and, but yeah, it's a little frustrating. Just feel like we're going, you know, like we just did fast. But we'll get through it better. Just like the bionic man. What was his slogan? Like better, bigger, faster. Okay, that's us. Yeah, I mean, I think the only thing that I'm a little further down right now is you're going to get, you know, we're going to get the second wave of people reaching out for help, which will come tomorrow morning.  So however we can communicate with once we make our game plan tomorrow morning of, you know, the priorities of the roads and stuff, somehow get that information out to people so they can start, okay, well, it looks like it's going to be a day for me, you know. Yeah, and that's going to be it. I mean, once we, you know, we're going to look at the heavier traveled routes. We need to look at any farms, any businesses that, you know, need to be, you know, they're impacted. So we had that issue after April 2019, any farms so that milk isn't being dumped, that you're, you know, getting the farm trucks in and out.  Okay. All right, yeah, just text me later. I will. What time do you want me to show up in the morning? Thanks, yeah, I probably, yeah, I will, I'm sure I'll get it probably when I hang up tonight. I'm sure I'm going to have several more emails. I've got 18 million text messages. Just tell Morgan if he needs any help tonight, just text me and I can come out and help him. Okay, I'll let him know. Well, again, thank you all for all that you do. Much appreciated. Oh, thank you. So it's always helpful if I, you know, getting the word out, we appreciate that. If you follow something on Facebook or however Facebook works, you like it, you, whatever. Love it. I don't spread it around. So that's always helpful to us is Facebook from Portmora and, you know, just trying to get the word out. So we always appreciate anybody sharing that. All right, anything further to take up with the board this evening? Not that I can think of, no. Anything else from the board member? Just a quick reminder, I won't be at the next meeting. Now let's talk about that. Are you going to come via Zoom or you're not going to be there at all? This is the one where I'm in the wilderness. Okay, I'm writing it down. No Lindley for real. No Lindley at all. Yeah, I'm writing it down. No. Okay. For real this time, no Lindley. All right. One of us may remember, we'll see. Okay. I'll put Denise in charge. That's right. Denise has got it. Are we going to reschedule this meeting to get the other items or just move them? They, oh yeah. I put it in the first part of my minutes I took, they are, they're, they tabled all the other issues to July 24th except for setting the tax rate. Okay. All right. Oh, I have one question. The energy committee is scheduled to meet tomorrow night at the town hall. Should that be rescheduled? I don't see why not. I guess it depends if your people can get there or not. There's nobody, there's nobody there now so. Yeah. Okay. I don't, I won't have any idea what that's going to look like tomorrow. Yeah, then maybe you want a message and postpone until next week just for, you know, safety. You got nothing pressing that has to be decided tomorrow. I guess. Right. Then yeah, you might want to put out a message out telling them, hey, you know what? Maybe we ought to give it a rest a week just to be safe. All right. All right. Thank you. Yeah, thank you. Yeah. All right. Anything else? If not, just need a motion to adjourn. Don't move to allow Teresa a nap and a good night's sleep. Yeah. I got a couple hours of sleep last night. Thank you. All right. Have a good night, everybody. Thanks, you too. Thanks, everybody.


So, last class we have considered a optimal control problem with constraint input and constraint in the state that problem we could not solve completely. So, rest of the portion rest of the problem we will solve it now. So, before that we will just recall the our problems that what is this, we have a optimization function objective function is minimize this what is called the control effort subject to the dynamic equation of the system and initial condition this. Our job is to transfer the initial condition the 0 1 initial condition by using a suitable control strategy. So, that it satisfy the our input constraint as well as state constraint to transfer the state from x 0 to final state x 1 t f and x 2 t f is 0 means that origin this is our problem. So, what we did is this unconstrained optimization problem, we have now that this is the constraint in input side and this is a constraint in state this state x 1 and x 2 which we have written into this form less than equal to form this. So, this 2 equation in turn we will get 3 equation in turn from here we will get 2 in equal to condition less than equal to 0 and we assume this x of t is differentiable with time. Then in order to solve this problem we introduce a state new state variable x dot x 3 dot t we have a initially 2 state variable. Now, we have introduce a third variable x 3 of t dot and that is form with the knowledge of the constraint which is less than equal to 0 from there we have constructing this state equation. This if you see this one equations 3 is 0 when all the constraints as specified here for x 1 x 2 if satisfied then this right hand side of this equation will be 0. If one of the equation at least one of the one of the constraint is not satisfied then we can write the equation 3 is less than equal to 0 for all t when the constraint 5 either it is satisfied or it is not satisfied either when the constraint 5 either is satisfied or not constraint are not satisfied. Then it is less than equal to 0 for all t at least one condition is not satisfied then it will be less than equal to less than 0 if all condition is then this is equal to 0. Then we specify the boundary condition for the new state variable x 3 x 3 0 is 0 x 3 t f is 0 then x 3 t is 0 for all t that from the equation we can write it this equal to 0 for all t x 3 expressions. Now, what is we have to do we will form our standard procedure to form a Hamiltonian function. So, h is form just as before we have discussed earlier once h is form then next step is the our case is del h del x is equal to del h del x we will come later del h del u is equal to 0 from there we got it u is equal to minus lambda of t this expression and our constraint on the input is the mod of u must be less than equal to 0. So, which in turn from this equation we can write it the mod of lambda t lambda of t is must be less than 1 then it will be a input will be less than 1 when there is no guarantee that lambda of t may be greater than 1 in that situation what should be the control input and that control input we have decided on the basis of that point region minimum principle that means we have to select you see this Hamiltonian function that one that Hamiltonian function is here you have to select that Hamilton that u is associated with lambda 2 again u is associated with lambda 2 lambda 2 into this factor will come. So, you have to use the choice of u in such a way so that that function value is becoming this product is becoming negative. So, on that basis of this if lambda 2 is greater than 1 then u must be switched on minus 1 because our control input cannot be more than 1 even if it is more than 1 lambda 2 then when it is less than lambda 1 minus 1 lambda 2 is less than 1 then you switch to plus 1 when it is in between then you switch to that whatever is the minus of lambda 2 suppose lambda 2 is less than 0.5 positive then you give the input the opposite sign of lambda 2. So, that means minus so our set function is generally the set function is 0 when x is greater than equal to 1 this is 1 when a mod of x is less than equal to 1 x of t is same x of t when mod of x of t is less than minus 1 it is minus 1 that is the set function is nothing but a this type of function saturation function this is 1 and this is is minus 1 and when this is also 1 slope is 1 when this if you can say that this is x of t when you have x of t greater than equal to 1 the output that this is you can say y of t the or that is actually output will be 1 when this is less than minus 1 that output will be minus 1 when it is x is in between x is in between minus 1 to that that will be the value of x we have to consider that this is.  So, minus sign when it is a mod of this less than equal to 1 that this is the u x of t, but it is minus. So, it is opposite minus of set function this indicates. So, then what you did it that our first condition we is delivered del h del h differentiate with x of t u is equal to 0 from there we got it u star is equal to minus lambda 2 of t. Then another state equation we will get del h del lambda t is equal to x that from that we got the three equations agree that three state variables are there including the new state variables then costate equation del h del x of t is equal to minus of lambda t. So, again we will get three equations then next is we have to use the boundary conditions agree to solve this problems and x 1 of t we know is 0 is given in the problem x 2 of 0 is 1 as is given in the problem, but our that initial state we have to drive to a origin with a suitable control x n keeping in mind that input is constrained and the state also constrained as given in the problem. So, our final state is x 1 t is 0 x 2 t f is 0 and x 3 from our boundary condition of x 3 is 0 x t f is 0 and another boundary condition from the free end point if you just consider the free end point another boundary condition we will get it that one the boundary condition that boundary condition condition for free end point system is h Hamilton function del s of del t this put the value t is equal to t f into del t f plus del s this del x t minus lambda of t that whole t f is equal to t f that transpose into delta x f is equal to this is the boundary condition free end points of the system in terms of Hamiltonian. Now, you see our terminal cost that s is 0 if you note delta t f is free delta t f is free, but delta x f is fixed that means delta f f is 0 and we do not have any terminal condition x as of 0. So, this term will be 0 whole term is 0 and this term also 0 and we have a this term also 0 we have left with this one is h of t h of this at t is equal to t f plus minus that one t f that has 0 and this term delta x of this is fixed. So, this term is 0 whole term will not come into the picture. So, this will be a 0 then we will put what is the Hamiltonian function and there we put t is equal to t f that is next step.   Now, look at this expression this here x t f value is what we want to drive the state form initial condition to the final condition this value is 0 then here is x 1 t f is also 0. So, only this term is there. So, from this one it is a half u star square t f and from there this is equal to 0 this part then from this part is plus lambda 2 t f into u star.  So, this term is not there and when x because it is a step input of x t f 0 this is also 0. So, this is 0 and this part is not 0, but whereas x t f is 0. So, this is u minus 1 that this the step input function is for the value of negative value of this one it is also 0 this is 0 and this is not 0 x t f is 0 this is not 0, but this value this is also 0, but this there is a minus 2 term t. So, this is also this quantity is if you see this quantity less than 0 this quantity also less than 0 and this quantity is 0 this quantity is 0. So, this will be the whole part will be 0 whole part will be a 0. So, now our is that one this boundary condition. So, from there you will see that is a lambda what is our lambda u is equal to what note u t f is equal to minus lambda t f that is we have our del h del h dot del u is equal to 0 from there we got it this one if you put this. So, this is the equation of this one our last equation if you recollect this one was that equation number 8 or 9 just check it. So, our last equation anyway this is the this is the equation from there you put it that is a lambda 2 t f square plus minus lambda 2 t f square is equal to 0 this is the lambda 2 t f square is equal to 0 this is the lambda t f is the lambda 2 square this. So, that is lambda t f lambda 2 t f is equal to 0. Now, you we can solve this problems we can solve this problem by considering the our boundary initial conditions of this one what is this one you see the from the basic state equation that our state equation we got it x dot when you are doing that what is called that x dot of t is x 2 of t then x 2 dot of t is equal to minus x 1 of t plus u plus u star of t which is equal to minus x 1 of t minus x 2 of t that we got it if you recollect this one was that you got it from the our state equation that this one if you see the del h del lambda is equal to that this equation this 2 3 equation and you see we have to keep the our state into the that in inside the constraint. So, if you put inside the constraint this then this quantity is 0 this quantity also 0 this quantity of the lambda x 3 dot is equal to 0 and this value is remain 0 for all t as we have considered the boundary initial and boundary condition of on x. So, we need only this 2 equation. So, that 2 equation you have written. So, this is the state equation we got it from del h del lambda of t is equal to x dot of t from there we got it now an x 3 dot if you write it you can write it is equal to 0 keeping that x 3 of 0 is 0 and x 3 of t f is equal to 0. So, this x t is 0 for all the time x 3 of this. So, we need basically this 2 equation then costate equation costate equation if you see the costate equation we also got 3 equation in terms of lambda 1 dot lambda 2 dot all these things and our costate equation finally, we will get it lambda 1 dot is equal to lambda 2 of t lambda 2 dot is equal to minus lambda 1 of t and now the third equation of lambda is lambda 3 dot is 0. So, now you see this 2 equals 2 set of equation and lambda 3 dot is equal to of t is equal to 0. Now see this also now x 1 x 2 lambda 1 lambda 2 dot all these things are you want to solve x 1 x 2 then it is you know you must have a information of lambda 2 then only you can solve it x 2. So, how to solve this one. So, our initial condition if you use this this one the solution of this 2 equation with the knowledge of this and this our solution is like this way x 1 of t is equal to twice sin t plus half lambda 1 of 0 into sin of t minus t cos of t. So, this is and this is this one minus lambda 2 0 t sin t solving this and this we will get it x 1 dot is this and x 2 of t similarly, you will get 2 cos t then half lambda 1 0 t sin t sin t t sin t then minus half lambda 2 0 sin t plus t cos t. So, this is this is the solution of x 1 and x 2 and lambda 1 and a lambda 2 solution we will get it lambda 1 lambda 1 of t is equal to lambda 1 0 cos t plus lambda 2 0 sin t and lambda 2 of t is equal to minus lambda 2 0 sin t and plus lambda 2 0 cos t. So, this now you see we cannot solve x 1 until unless we know the lambda 1 0 value lambda 2 0 values similarly, x 2 also. So, lambda 1 0 lambda 1 0 value lambda 2 0 value we must know it again. So, how to solve this equation so now and we have a one boundary conditions also there if you see this boundary condition we got it lambda 2 t f is equal to 0 the boundary condition Hamiltonian boundary condition free and point boundary condition we got it that one. So, now we have to solve this one you must know that this are two unknowns are there x lambda 2 0 lambda 1 0 lambda 2 0 and you do not know that what is called here also lambda 1 0 lambda 2 0. So, find next is find lambda 1 0 and lambda 2 0 and t f because you have to drive this straight from initial condition 0 1 to final condition 0 0 in time t f. So, t f also you unknown so how to solve so using this n condition what is this n condition this is one n condition another n condition x of 0 or x of 0 is equal to 0 x of 2 0 is also 0. So, now use x of 1 x of 1 t is equal to 0 this equation. So, let us call this equation number is some equation number is a this is the equation number b. Using t is equal to 0 in equation using t is equal to 0 x 1 0 is equal to 0 x 2 0 is equal to 0 in equation in equation a and b a and b we get two equations. So, another equation we will get it at t is equal to t f we know. So, you put the value of a 1 that this condition is a and b this we know x of t x 1 0 is 0 and x 1 this or not 0 at t is equal to t f t f at t is equal to t f we know t a t is equal to t f this x x t f is equal to 0 x 2 t f is equal to also 0. Using t is equal to t f this so in equation 1 and 2 we will how many equations will unknowns are there in equation 1 and 2 we have a three unknowns are there. You see one unknown is there t f is unknown lambda 1 0 unknown lambda 2 0 unknown, but we have a two equation we need another equation what is called that lambda t f lambda 2 t f values is equal to 0 and use the lambda 2 f value equal you will get another equation agree.  So, from this equation a and b two equation I am getting from this is another equation let us call this three equation solving these three equation we will get the values of lambda 1 0 we will get the value of lambda 1 0 lambda 2 0 and t f then easily we can find out the solution of x 1 x 2 and x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 all these things and we and also lambda t lambda 2 t. So, we monitor the lambda 2 when it is a the mod of lambda t is less than equal to 1 then we will switch that u of t when mod of lambda 2 of t is less than equal to 1 then we will take u star of t is equal to minus lambda 2 of t then when it is a greater than 1 this is when mod of lambda 2 is less than equal to 1 then this equal to lambda is equal to minus 1 when lambda 2 of t is greater than 1 then it is minus 1 and you will switch to 1 when lambda 2 is less than minus 1 see that equation according to this we have just switched this one if you recollect this one here this thing we have used it here once you know the lambda t expression. So, lambda t expression I can know once you know lambda 0 to lambda 0 expression then you know what is lambda 0 t of this I think this is the lambda 1 of 0 that that one lambda 1 of 0. So, this you can do it and then you can implement the control that will drive at t is equal to t f that will drive the initial state to a final state at origin. So, this is all about your what is called the solution of that optimal control problem with constant input as well as constant in the state how you have to solve it. So, next we will discuss about the norms the new topics is a norms the norms of a norms for vectors matrices then your signals and systems means linear systems linear systems this norm. So, the norms basically the norms gives an overall measure of the vector size of the vector. So, that norms is a norms it gives an overall measure of the size of a of a one vector matrix signal systems then is systems this norm is often useful for measuring for analysis the for analyzing the growth of numerical examples that norm we generally use for analyzing the growth of what is called numerical errors involved in the process of iterative process again. So, let us call the norm of a vector norm of vectors it is often useful when the norm analyzing growth of numerical errors. Let us call how to find out the norm of a vectors there are different norms different context it is used. So, let us call we have a vector let us call we have a vector whose dimension is n which is written as x 1 x 2 elements of these vectors is x n. So, this is a vector is dimension n cross n n rows one column and this form form a vector space vector space called r cross 1. That means we can short we can write x belongs to vector space r cross one dimension agree that dimension is n cross one. So, now this are the elements of this vector whose dimension in n cross one and that x 1 x 2 is a constant for the time being is a constant elements. So, what a definition of p norm of a vector is denoted by double line whose it is a vector x n 1 by n double line and this p is defined as summation of i is equal to how many elements are there and elements are there. So, x i mod absolute value of each element x 1 x 2 dot that x n you take it then to the power of p whole to the power of 1 by p. So, this is called p norm of a vector that means how many elements are there you take the absolute value sum of absolute value of the elements whole to the power of p then 1 by p p th square root of this one you do it. Now, let us call most frequently we use the norm 1, norm 2 then it is called infinity norm. So, most frequently we use l 1 norm which is also called that one norm this is also called one norm of a vector of a vector of a vector and this symbolically it is represented by x of this suffix 1.  So, it is nothing but a summation of i is equal to 1 to n mod of x i this p is 1 or here you can write for p greater than 1 greater than equal to 1 less than equal to 1 or if or you can write it p is equal to 1 to dot dot dot this p is equal to 1 to this. So, here for p is equal to 1 that it is called norm of a vector. Now, this is you can think of a norm of is suppose you have a set of equation is there you want to solve it by iterative method. Then you the variables are let us call x 1, x 2 dot dot x n variables are there you are solving the a set of simultaneous equation. Now, you absolute value of x 1, x 2 whether it is a convergent or not here. So, present value of x 1 let us call it is at this e 1 is the present value of x 1, present value of this is the present value of x 1 minus the old value of x 1 this is the old value of and that is I denoted by e 1. Similarly, for x 2 now I am putting i, i is where is 1 to n. So, if I take the norm 1 and l 1 norm that means 1 norm of a vector e, e how many components of e are there u 1, e 2 dot dot e n because we have n variables. So, some of the all errors you make it and if you less than 10 to the power of minus let us call 4. Then you stop your iterative process that means it indicates that all the values at least it is to the value 10 to the power minus 4 all the values of e 1, e 2 because I am putting some of all e 1, e 2 there. So, some situation if it is a iterative method and norm 1 also they use it. Next is your norm 2, when is norm 2 it is nothing but a p is equal to 2 this l 2 norm or it is called or it is called 2 norm of a vector of a vector or you can say or l 1 norm or it is called 1 norm of a vector. So, our 2 norm of a vector is what this denoted by x 2 this 2 and which is nothing but a your summation of i is equal to 1 to n mod of i this square whole square root 1 by 2. Here for p is equal to 2 this has a some meaning and this is also called this norm also called is a eclinion norm or it is called distance is basically if it is a 2 dimensional case x 1 square plus x 2 square square root of this 1 and it is nothing but a the distance or length of this vector. Suppose in a 2 dimensional case if your x 1 is here x 2 is this x is if it is this point was x 1 and x 2 and this is nothing but a denoted by x norm of 2 that means length of this vector is nothing but a eclinion norm or the 2 norm of a vector. Again this is also one can use for what is called to find out the what is called in iterative method also you can use this norm to check it whether the algorithm has converged or not or this next is your l infinity l infinity norm or it is simply called infinity norm. What is this infinity symbolically it is represent by x is this one and this when p is infinity that means in that expression p norm expression you what you write x 1 to the power of infinity x 2 to the power of infinity. If x 1 let us say that x 1 x 2 I told you the numerical value if x 1 is less than 1 then x 1 to the power of infinity is 0. Suppose x 1 is greater than 1 this is infinity out of this which is x 1 x 2 all this thing out of this which magnitude is the greatest and it is greater than 1 that information is enough to find out the infinity norm. So, the infinity norm I am repeating is max i mod of x i and i varies from 1 1 2 1 2 dot dot n out of this which one is maximum you take that is the infinity norm of that one logic is this one if you just see the this situation of that one again suppose we have a 3 variables are there x 1 x 2 we have a 3 variables x 1 x 2 x 1 is less than 1 x 2 is let us call is 2 x 3 is 5. Now, you see x 1 is less than 1 to the power of infinity it is 0 x 1 is greater than 1 let us call 2 to the power of infinity and then it is a x 2 which x 3 which is a let us call 10 greater than 1, but then to the power infinity also infinity. So, you are what we are considering the maximum value of x y is considered to find out the infinity norm of a vector this and you see this power multiplied by the 1 by p. So, this this cancelled of this one if you can think of it some of all these things because basically k u is you make it some of the all these things which one is highest you keep it then you pit it highest magnitude of this one p into p p p cancelled. So, it is a ultimately it is coming max i 1 to p dole absolute below of x i you have followed my point this one this if I write it let us call x 1 x 2 and x 3 x 1 value is 0.5 x 2 value is 1.5 x 3 value is 3 then what we will write it that p values of this is summation of x 1 means 0.5 whole to the power of p 1.5 whole to the power of p 3 3 0 whole to the power of p whole 1 by p this is 1 by p. Now, this is equal to 0 when p is infinity this is compared to this this is is because this is the greater than this one. So, you take it the whatever the absolute value of maximum that one. So, this and this cancel only 3 maximum value of from all the components what is that is the infinity norm that is why you are writing it that one. So, this is the you call it the infinity norm of a vector. So, next is called the norm of a matrix similar way we can define the norm of a matrix. So, first is is Frobenius norm it is defined for matrices by treating the matrix elements the matrix elements.  So, the Frobenius norm is defined you that matrices all elements you put it into vector form. That means this vector below this one you keep it this column vector below this one you keep it the next column vector in this. So, whole thing will be vector of dimension n cross this whole thing will be the vector of dimension m into n cross 1. That means this vector below this you keep it this one below that one keep it third column below this one keep fourth column in this way and you will get a matrix m into cross 1. Then Frobenius norm is nothing but a sum of absolute value of all elements square sum of all elements square square root of sum of all elements square. So, Frobenius norm is nothing but a we denoted by this a m cross n of f stands for Frobenius norm is equal to summation of i is equal to 1 to m summation of j is equal to 1 to n m is the number of rows this one and a i j square. So, absolute value is not necessary because it is a square of that one this summation of all elements you take it then take the square root of this one. So, it is like if you see it is like is what L 2 norm it is it is L 2 norm of a matrix you can say L 2 norm of a matrix just like L 2 norm of a vector it is L 2 norm of a matrix is called the feminist norm. Next is your that L 1 norm of a matrix the same as the L 1 norm of a vector. So, that is denoted by a m cross n of 1 is equal to maximum j then summation of mod a i j this i is equal to this is j i is equal to 1 to m and j is equal to what 1 to n because our dimension m cross n. So, you take j is equal to 1 i varies 1 to m you calculate all summation then j is equal to 2 means second column all the elements absolute sum you do it. Third column j is equal to 3 third column absolute sum of all these things you do out of this which one which column absolute sum is maximum that is called the L 1 norm of a matrix. So, this is nothing but a maximum column norm column sum maximum column sum. So, if your matrix if you see what will that L 1 norm this column you absolute sum of this you do it that column absolute sum of this all elements you do it and in this way you proceed up to nth column out of this which one is the maximum value that will give you the L 1 norm of a matrix that is why it is called maximum column sum. Then L 2 norm L infinity norm next is L infinity norm of a matrix L infinity norm of a vector is L infinity norm of a vector is what we have seen L infinity norm of a vector the maximum value of this element of a vector. Similarly, here also L infinity norm of a matrix m cross n is equal to this L infinity is equal to maximum i is equal to 1 comma 1 2 comma dot dot m summation of j is equal to 1 to n absolute value i j this. Now, i is equal to 1 where is j is equal to 1 to n that row first row i is equal to second row out of this all row wise your sum out of the absolute sum then what are out of this which row is the maximum absolute value of the sum that is called the h infinity norm of a matrix or it is that is called L infinity norm of a matrix. So, that is called your also called maximum row sum this has a similarity with the L infinity norm of a vector L infinity norm of a vector L infinity norm of a vector what is telling you take the absolute value of all the elements then you picked up which value which element have the maximum absolute value that is the L infinity norm of a vector. Similarly, here also your row wise you take the absolute value of this one out of this which one is maximum that is the L 2 norm of a matrix. So, next is L infinity norm sorry L 2 norm of a matrix is defined as a m cross n 2 is equal to lambda max a transpose a then square root of that one that means a is a rectangular matrix you see a is a rectangular matrix and if you do a transpose that dimension is to be n cross m and this dimension I know it is a m cross n. So, it will be a square matrix n by n. So, n by n you will get the square matrix of that one you find out the absolute maximum value of this matrix and take the square root of this is a symmetric matrix all Eigen values are will be positive non negative number. In other words all Eigen values are non out of this which Eigen value is maximum you take the square root of that one.  So, this is all about the vector and matrix norm what are the norms you have to P norm then a feminist norm is nothing but a L 2 norm agree and this or you can do not write it this L 2 norm we write it feminist norm and this is nothing but a L 1 norm h infinity norm L 2 norm this. So, you take an example and verify all the norms how to compute example and this is you can write it is equivalent to a L 2 norm of a vector the way you are doing agree the way I told you that whole elements of the matrix is whole elements of the matrix you convert into vector form then find out that vector L 2 norm. So, this is equal to L 2 norm of a L 2 norm of a vector instead of you write it L 2 norm of a vector when the matrix elements are arranged into a vector form. So, do the example of that one x we have a vector whose dimension is 4 cross 1 is given 0 minus 10 to 1 and a is given 1 0 0 0 5 minus 10. So, this is the value of the matrix agree. So, find out if you find out the one norm of a vector one norm of a vector means some of all elements absolute value that will come 13 that means 10 absolute value then 2 absolute value 1 absolute value is 1 that will be 13 then x 2 norm is nothing but a square of this one then 0 square plus 100 square 10 square then 2 square plus 1 square whole then square root of this one that will come root over 105 agree and next is infinity norm of a that infinity norm that infinity one out of this which magnitude is maximum that means that transpose you can write it that will be the 10. And next is that your matrix A matrix norm A fabulous norm agree this one is you have arranged in the all vector one and some of the all things then it will be coming if you see this one and this will be summation of i is equal to 1 2 3 summation of j is equal to 1 2 3 then mod i 1 j square and whole to the power of this is the fabulous norm to the power of this is the fabulous norm and that value is coming near about 126 to the power of half then a 1 norm a 1 that means 1 norm of a vector l 1 norm or 1 norm of a vector is equal to what maximum column sum maximum column sum is what this is 1 this is 15. So, this will be a 15 or you can say maximum maximum column sum then this is a 2 a 1 and this is a 2 a 1 and this 2 infinity a 1 2 infinity is your maximum row sum is 10 maximum row sum then l 2 norm of a matrix what is this square root of lambda max a transpose a that means that quantity and this quantity a 2 norm this quantity if you do the multiplication this will come your 125 square root of this one that this lambda maximum lambda maximum again value of a transpose a is 25. So, that square root of this one will come 11.18. So, this is the example form how you will find different norms l 1 norms l 2 norms and a l infinity norm always and in case of matrix is a Frobenius norm is what is same as l 2 norm of a vector. So, this is I will stop it here today and next class I will discuss the what is signal and what is system how signal norms physical interpretation of signal norms and system norms that we will discuss next class.


sound or share. Okay it is Ivan here with you on a Friday evening. We're broadcasting right across the northwest of Ireland and of course beyond on HighlandRadio.com and bringing some news right now if you're a fan of the legend that is Elton John. This news just breaking in the last little while. Elton John is to headline Glastonbury Festival next summer. Glastonbury will be his final UK show for Elton John's last ever tour as he's playing Glastonbury next summer playing the last ever UK date on the farewell tour. The BBC reported that the singer will top the bill on the pyramid stage on Sunday, the 25th. Not the legend slot on Sunday afternoon. No he is topping the bill. Statement read announcing this show that Elton John says there's no more fitting way to say goodbye to my fans. I can't wait to embrace the spirit of the greatest festival in the world. It's going to be incredibly emotional. That's what Elton John said earlier today and let's see the festival genuine enthusiastic support for the best emerging talent is something I've long admired. So he's looking forward to headlining Glastonbury next summer. The show will come more than five years after Sir Elton so 75 now it's going to be 76 next summer. He announced his 350 date farewell Yellowbrick Road tour. It was originally due to wrap up in 2021 but multiple dates had to be re-scheduled due to of course the pandemic and also Elton had a hip injury as well. So Sir Elton is recently wrapped up the US leg of his tour with a three night stand at LA's Dodger Stadium. Of course he famously played back there in the 70s and in the 80s as well. So it's all come full circle for Elton John. The Glastonbury gig will come at the end of the UK leg of Sir Elton's farewell tour which kicks off in Liverpool next March and after Glastonbury's only seven more dates to play in Europe before he retires from Turing forever. So there we go if you're a fan of the legend that is Elton John the big rush for tickets of course the tickets sold out within an hour and they went on sale last month but there is some more tickets on sale in January. So it was his legendary song. Tiny dance.