So, last class we have discussed that if you have a given a functional j is equal j dot is equal to t 0 to t f and v of t x v is a function of t and x t and x dot t. And if you consider the one point is fixed and other point is free then in order to have in our job is to find a trajectory optimal trajectory x t such that this functional is x has is its extremal values either minimum or maximum. So, the necessary condition we have derived is this one. So, the first condition is the Euler's Lagrange equation this equation is Euler's Lagrange equation. So, you have to solve this one you have to solve this one there are two conditions a boundary conditions are there this condition when t f is free when t f is free then you have to use this equation. And x f is x t f is fixed then out of this one only this is you have to use it when x t f is free, but t f is fixed then you have to use in addition to the Euler's Lagrange equation. When both are free that means x t f is free and at t f is free then we have to solve Euler's equation in addition to the two boundary equation boundary condition. And this two boundary condition is called the transversality condition agree that we have seen it. And we have consider the different cases if you recollect we have consider the different cases case a b and c different cases and correspondingly Euler's Lagrange equation you have to solve it and the corresponding boundary condition. Further we have consider the next is we have consider the case 4 when the end point is restricted on a curve which is the function of t agree this. And in this equation that you will get a what is called transversality condition one is that x dot of t instead of x dot of t minus g dot of t at t is equal to t f this equation you have to solve. So, this is we have to now after solving this equation that we will get the trajectory whether this trajectory is what is called optimal this trajectory will maximize or minimize this functional or not that we have to check it by using the what is called sufficient condition. We will now discuss that sufficient condition for the functional j is to be optimized what is the sufficient condition for the functional j will be optimized mean either maximum or a minimum value of the function. So, our sufficient condition sufficient condition it is same as what we discuss in case of what is called the static optimization for problem for multivariable optimization problems the same condition will consider here also sufficient condition. The sufficient condition will give you whether the functional is maximum or the along the trajectory if you use in the functional that whether it will be maximum or minimum value of the functional that will give you the you will get it from sufficient condition. So, if you see this our second variation of the second variation of the incremental what is called functional that we have denoted by del j square and that is equal to if you see the Taylor series expansion of what we have discussed earlier that means that incremental functional value the second we have we will consider up to second derivative of the Taylor series expansion. And that second derivative we will consider now as a what is called the second variation of the functional that is equal to integration of this t 0 to t f and then del x of t that whole transpose del square v dot del x square of t this is a this is a matrix because we are finding the gradient of v with respect to x again we are differentiated with respect to x. So, this is the matrix so that matrix multiplied by delta x of t vector. So, this and second term the second term is twice delta x of t whole transpose then delta square v differentiate gradient of v with respect to x then x dot or reverse order x dot this you calculate along the trajectory of this gradient multiplied by delta x dot of t. Then plus delta x dot of t delta x of delta x of dot of t transpose delta x dot of t transpose this delta square v dot delta dot square of t this compute at the this is the matrix computed along the trajectory star means along the trajectory delta x dot of t that this bracket and this bracket is complete this and this complete and then differentiate with respect to t. So, this quantity inside the bracket of this one is a scalar quantity so we can write it in terms of quadratic form that you know quadratic form is nothing but a x transpose p x form we can write it. So, how we are writing this one you just see this one this integration of t 0 to t f then we have a delta x of t then delta x dot of t. So, this is a matrix form you write it vector in case then you write it this del square v dot del x square of t then del square v dot del x of t into del x dot of t then del square v dot del x of t into del x dot of t del square v dot del dot square of t that is whole matrix agree this you evaluate along the trajectory multiplied by delta x of t multiplied by delta x dot of t. Now, see this one this is a matrix of dimension if x is a dimension of n variables then this is the matrix of dimension n cross n this is n rows n column this is also n rows n column n rows n column and similarly the whole matrix dimension will be twice n into twice n if you see similarly this one is a n rows n column this whole thing. So, now in order to this whole thing differentiating with respect to dt with respect to dt this whole this is a vector matrix multiplied by column vector then differentiate with respect to this whole quantity is a scalar quantity same as this one. Now, in order to that we know that sufficient condition of a second variation of the functional must be if it is greater than 0 if it is greater than 0 then the functional value along the trajectory what we got it should be a negative sorry it should be a minimum value of the functional. If it is a delta square v is less than 0 then functional value along the trajectory will be a maximum value of the functional. So, how to decide this one if you see it is now in quadratic form. So, our this matrix compute this matrix whose dimension is twice n by twice n along the trajectory if this matrix is positive definite matrix this matrix is positive definite matrix that indicates that del square del j square means second variation of the functional will be positive value means the functional value along the trajectory is minimum. So, our condition is if delta square j is greater than 0 if the matrix delta square v delta x square of t delta square v delta x t and delta x dot of t delta square v delta x of t delta x dot of t this order may be changed delta x dot and delta x this value will be same. So, it does not matter for this one we have discussed this thing in details while we have discussed the static optimization problems. So, this x dot square of t compute this matrix along the trajectory and if it is a if you want to delta square is greater than 0 implies this must be greater than 0. So, we will check this matrix whose dimension is twice n into twice n where x is the n variables of the what is called functional if this matrix is positive definite implies that delta square j is greater than 0. That means the functional value what will get again if you put this x star that means optimal trajectory in the functional values then we will get it minimum value of the functional and if you can write delta square j is less than 0 if that same matrix that this matrix this matrix is less than 0. This implies that the functional value j star of this is maximum value along the trajectory. Similarly, this implies the j star of this is the minimum value along the optimal trajectory you can write optimal trajectory means x star of t this is x star of t you can write it. So, this is the sufficient condition for this one again. So, now let us solve one problems to get how one can solve such type of optimization problem dynamic optimization problem using the calculus of variation principle. So, example taken example, so find our problem is find the extremal for the functional j is equal to t 0 to t 0 is equal to 0 to t f and this functional is given x dot square plus 24 x of t into t d t. So, this functional value j is to optimize extremal whether minimum or maximum that we have to find out and corresponding what is the trajectory for this one. So, where left where the left end point is fixed end point is fixed in other words x of t 0 is equal to 0 at x of t 0 is 0 and t 0 is equal to 0 here t 0 is 0 that means you can write it t 0 is 0. So, this point is fixed point you can assign this point as a this point is fixed point and the right end the right end point t f is free, but x t f value is equal to 2 is fixed x t f value whatever the t f value is the free, but x t f finally, this trajectory should reach at time whatever the time is there at 2 units it may reach. So, corresponding to our problem if you represent that one it is something like this. So, if you consider x star of t and this is x star of t near about delta near about the optimal trajectory there is another trajectory which you call x star of t never would of the optimal trajectory is this. We are calling it a point and this point is b if you say that point is t f is free, but x t f what is the x t f is fixed that is 2 x t f is equal to and we have to find out x star of t the optimal trajectory for this for the functional for which the j will be extremal whether minimum or maximum that for that we have to check the sufficient condition. So, if you just follow our methods what we have to say first we have to consider our step solution. So, first you write the v function v function is what in your case 2 x dot square of t see this is our v is a function of x t x dot of t and t. So, the v function is what function of v is x 2 24 x of t into t this v. So, write the Euler's equation if you recollect the Euler's equation del v del x of t minus differentiation of del v with respect to x dot del x dot of t partial differentiation of this one. Then this equal to 0 and since x is a in this case dimension is 1. So, this dimension will be 1 cross 1. So, I will just put the value of v and differentiate with respect to x that is our next problem. So, v is then if you differentiate with respect to this x I will get 24 t first part of this Euler's equation this is called the Euler's Lagrange equation. Now, second part of this one you see we have to differentiate with respect to x dot. So, that will be a your 4 x dot of t is equal to 0 then 24 t is equal to 4 x double dot of t is equal to 0. Then your case is x double dot is equal to x double dot of t is equal to 6 t which equation number 1. This is a simple differential equation. So, I will advise you to recap the solution of differential equation in presence of forcing function that you recollect this one. Since this is a simple case one can find out the solution of this one by using what is called double integration. If you do it first time you integrate it will get one constant term second term you integrate it will get the another constant term all this. So, you can this in this case it is very simple. So, I can write the general solution of equation 1 the general solution of 1 what you can write a general solution of this one x of t is equal to c 1 t plus c 2 plus t cube for your convenience. Just I show you the x double dot of t is equal to 6 t integrate both side integrate both side x double dot t d t with respect to t t integrate 6 t d t then you will get x dot of t is equal to 6 into t square by 2 plus c 1. Then again you integrate this one once again if you again integrate that x dot of t again integrate with respect to time t then 3 integration of t square d t plus c 1 integration of what is called d t. So, if you do this one that solution is x of t is equal to t square t cube by 3 it is cancel 3 3 cancel the t cube we got it then you have a this c 1 into t this one and another integration constant you will get c 2. So, this is the general solution of that one let us call this is equation number 1. So, now let us try if you differentiate this one once again then what you will get it that c 1 into t differentiate 1 this c 2 is constant this is 0 then 3 t square let us call this equation is 3 equation 3. So, now this is the Euler's equation from Euler's equation we got the what is called trajectory optimal trajectory of this one but still it is with us that how to find out c 1 and c 2 that is and that two constant we can find out from what is called the initial that of a boundary condition using the boundary condition. So, let us see that how one can find out that c 1 and c 2 of equation 2. So, at time t is equal to t 0 that is 0 let us see what is our trajectory t 0 value. So, this is equal to c 1 into t 0 t is equal to t 0 plus c 2 into t 0 cube t is equal to t 0 then c t t 0 is 0 this is 0 this is also 0. So, c 2 value is 0 the constant c 2 value is 0 now initial condition from the initial condition we got the condition of this then next is at time t is equal to t f t f is unknown is free then from equation 2 this is from 2 we can write it x t f is equal to c 1 t f plus c 2 value is 0 we need not to write it here t cube this. So, c 1 that this value is given to the problem is 2. So, now our c 1 value is what we can write it c 1 value is your t f c 1 value 2 minus 2 take it this side t f you take it this side then t f cube divided by t f. So, this is the value of c f, but that depends on the final time t f because t f is free for this. So, let us call this equation is equation number 4. So, now this is the condition that means c 1 value we know c 2 value we know. So, the description of our optimal trajectory is known provided if t f is known that what type of t f that will reach to the our x t f is equal to 2. So, now cost condition is coming transversality conditions transversality conditions. So, our x t f if you recollect this our terminal conditions that one x t f is fixed that means delta t x t f is 0. So, this condition will not come into the picture only this condition will come Euler's equation and that this condition will come into the picture because here x t f is fixed not free, but t f is free that a t f means delta t f is not equal to 0 this implies that this boundary condition must satisfied that we have explained earlier. So, let us see this one f x t x dot of t of t minus and if you recollect this one see I have not put it star you can put it star because whatever solution you will get it that is only optimal trajectory star. So, it not necessary put it star that if you get the solution of Euler's Lagrangian equation you will get the optimal trajectory x star of t or you can write x of t this one. So, I am just not writing if you like you can put it star also there. So, this and del v the transversality condition when t f is free, but x delta x t f is fixed delta x t f is fixed means delta x t f is 0 then this is equal to x dot of t whole this I should write it transpose if x is a vector, but it is a scalar. So, not necessary to write transpose for this one. So, this into x dot of t, but do not forget to compute this one as t is equal to t f you have to put t is equal to t f in the transversality condition see Euler's equation transverse t is equal to t f. So, do not forget to write t is equal to t f when the t f is free. So, this now write this equation the delta x is 0. So, this is the v of x is equal to x dot square of t plus 24 x of t into t. Now, this you differentiate with respect to x dot that means this is the v we have differentiate with respect to x dot means this is a 4 x dot bracket 4 x dot of t into that other term is 0 because I am differentiate with respect to x dot. So, it is a x dot of t is equal to put t is equal to t f is equal to 0. Now, see this one that is a 4. So, there is a 2 you divide by this into 2 then it will be x dot t is equal to t f. I am now putting the t values t is equal to t f plus 12 x t f into t f minus 2 x dot t is equal to t f square this is square I missed it. So, this is equal to 0. So, finally therefore, x dot square t f is equal to 12 x dot t f is equal to 12 x t f into t f I am correct. So, this is a 4. So, this is I am writing x 2 x dot square 24 x t f so 24 t f. So, 4 that is your x dot 4 x dot t into x dot. So, it is a twice of this one. So, if you take it this that side left hand side. So, it is a minus of this equal to 0. So, this is minus. So, now I know this value of what is called t f x value x solution of this is here solution of x dot you see solution of x dot I know that c 1 3 sorry c 1 x dot is x dot. So, x dot t is c 1 3 t square as t is equal to t f as t is equal to t f x dot t f c 1 3 t f square. So, I will write x dot value is c 1 plus 3 t f square whole square minus 12.  So, this is 12 into 2 into t f is equal to 0. So, if you simplify that one c 1 square c 1 square 9 t f 4 x dot 4 plus 6 c 1 t f minus 24 t f is equal to 0.  So, now c 1 expression already we have derived the c 1 expression if you see in terms of t f. So, I will put the value of c 1 expression 2 minus t f cube by t f in this expression. So, if you put this it is in this expression then what we will get it just see this one I am just putting this in this expression. So, c 1 is what 2 2 t f cube by t f whole square this is c 1 this value is c 1 this value is c 1 plus 9 t f 4 plus 6 c 1 is what 2 minus t f cube 2 minus t f cube divided by t f into t f square minus 24 t f as it is minus 21 t f as it is look in the if you see this one this is the equation of this one I am just putting the value of c 1 and where c 1 is c 1 is 2 minus t f cube by t f this is c 1 minus c 1 this value c 1 I am putting in this expression and then I got it. So, if you simplify this one if you simplify that one finally, we will get the expression. So, I am skipping few steps for the there is a just is some academic exercise you have to do it to arrive in this expression. So, t x this t f 6 4 t f cube plus 1 minus 1 is equal to 0. So, now, this is the equation which one can solve for t f let z is equal to t f cube. Now, if it is this one I can write it that this t f expression that z square minus 4 z plus 1 is equal to 0. So, z is equal to it has a two roots quadratic form in fact, it is a you will get it how many roots is here for the time being z I am getting it minus b means 4 plus minus root over b square means 16 minus 4 a minus 4 a minus 4 a minus c divided by twice a. So, that will be 2 plus minus that is root 3. So, it is a 12 2 is taken out then this.  So, our t f is related t f 1 from z 1 if you see z 1 is equal to t f cube t f 1 cube is equal to what we got it that is 3.732. So, t f 1 is equal to 1.551 this one and z 2 another case is z 2 z 2 is equal to t f 2 cube which is equal to 0.2679. So, t f 2 is values is your 0.6446. So, there are 2 final time is there 1.5 times the state will reach x t f is equal to 2 another time is 0.2679. So, t f 2 is values is your 0.6446. So, there are 2 final time is there 1.5 times the state will reach x t f is equal to 2 another time is 0.26.6446 the our final state will reach to 2 units agree.  So, that value will come minus 1.117 this is equal to 2 minus t f 1 plus for another case for t f is equal to or you can say what is our trajectory x t of this is equal to c 1 t plus t cube and I know c 1 value c 1 value 1 case is minus 1.117 t plus t cube. So, this is the optimal trajectory for this one when at time t is equal to 1.551 second this x t f 1 will reach the state is variable is 2 units. This is one solution and if you plot it let us call your advice to plot this x t versus that time agree and that trajectory at time that trajectory let us call is some name you give it curve 1 that trajectory is called curve 1 curve 1. Now, next situation that is what we will see that is for t f is equal to our time is that for t f is equal to t f 2 that is our time is what if you see that t f is equal to t f 2 that is what we have got it that 0.6446 second agree then c 1 this implies c 1 is equal to twice minus t f 2 cube divided by t f 2. So, this value will come 2.6871 constant. So, corresponding trajectory optimal trajectory that x t is equal to c 1 t plus t cube. So, it is c 1 is 2.6871 t plus t cube agree. So, it is c 1 is 2.6871 t plus t cube agree. So, you are once again you are advice to plot t versus time and call this curve that this optimal trajectory curve is curve 2. You can easily plot it this t versus t is 0 to you know how long you have to plot it this is valid for t is equal to t f that value is your 0.6446 second you plot it up to this t is equal to 0 to this. And that one you plot earlier one t is equal to you have to plot this plot you do it t is equal to t f 1 which is 1.1551 second agree. So, you have to plot t there are 2 trajectories are there. Which will give you optimal value or external value of the function? Both are what is called optimal trajectory. One case you justify your think 1 case will give the maximum value of the functional. Other case it will give you the minimum value of the functional out of this 2 trajectories. One will give you the maximum value of the functional other will give you the minimum value of the function both the trajectory reaches is final value at x t f is equal to unit is 2 units, but different times this one. So, I adjust advice you make your comments make your comments on the curve on the curve 1 and 2, which I asked you to plot it and make your comments which one is giving the optimum in the sense maximum value of the functional which trajectory will give you the minimum value of the functional values. So, the whether minimum or maximum value functional will give you you can find out how that our sufficient condition sufficient condition you use it. What is the sufficient condition if you recollect this one that our matrix that Hessian matrix if you recollect in static optimization problem we have discussed as an a Hessian matrix. The Hessian matrix is del v dot del x square of t del square v dot del x of t into del x dot of t del square v dot del x of t into del x dot of t del square v dot del square del x dot square of t. This value you find out the trajectory x is equal to x t is equal to x star of t what is x star of t one case we got it x star of t. If you see first case when t f is equal to 1.5 second we got it minus 1.117 t plus t cube when t f is equal to t f 1 is equal to 1.15 second. So, you put this values because in this expression you differentiate with respect to x gradient v gradient you find out with respect to x.  If it is a positive definite matrix if this is positive definite matrix then functional j star is minimum value we will get. If this is less than 0 then j star is we will give you the maximum value of the functional. So, this way you can check it. So, this we have shown it how to solve a problem dynamic optimization problem by using the calculus of variation concept. So, now we will see slowly we will go to application of what is called calculus of variation to a control problems. The control problems means you have a dynamic system any system one can model into a mathematical model as a transformation model or state phase model or different model. Our problem is concentrated to describe the dynamic system in terms of differential equation. In terms of differential equation let us call if the dynamic system is described by nth order differential equation one can convert by selecting the suitable variables into convert the differential equation which is order of n can be converted into a nth first order differential equations. So, that is called is a state phase representation of a dynamic systems whether the dynamic system may be linear or non-linear, but we can apply the what is called the calculus of variation principle to find out the optimum value of the functional or objective function optimum value. Let us see how to do this that one. So, now application of you can say the application of calculus of variation approach to optimal control problem solution. So, that is our problem let us call consider our system or plant consider the system the dynamic system or plant is described by x dot capital X. I am now using to represent if the variables are more than one then I am represent with the capital X. So, let us call that variable is n cross small n cross one n variables are there. So, that is a function of X t U t and function of time. So, this function also we have a n function that there is a vector. So, let us call this is equation number one and if you see that vector dimension is n cross one and we assume that we have a m inputs are there to the system. So, this is the time. So, this is a description of what is called our dynamic system in terms of variables and how many variables are there n variables how many inputs are there m inputs. So, our problem is that you find and corresponding performance index or objective function corresponding performance index or objective function is j is equal to s function of X t of t and that X t is equal to t f X t f or you can write it here better you write t is equal to t f the terminal time that this function below this is a scalar one because objective function is a scalar one.  So, and this we call this term first term is called terminal cost terminal cost and this s is a function of X of t and t it is differentiable with respect to time and t that is and that function is a continuous function and this term is called the cost integral cost function and that j is your performance index. So, our objective is if you see our objective is to find a control signal in the system suppose we have a system is there that system and we apply the input U of t and the output is let us call the states at the output. So, we are accessing the states our problem is to find a control input U of t such that this performance index what is the performance index that performance index is indicating that it is indicating 0 to t f and it is a function of X t U t and t U t is the control input once the control input is that is that regulates the state X of t agree. So, this plus the terminal means X time t is equal to t f what is this function value that is called the terminal cost. So, that means we want to drive the state at final state at particular point agree and that represents in terms of a quadratic form agree it is we cannot write the X t f only it is quadratic, but that quantity must be a positive quantity or 0 or 0. So, our problem is find a control input which is which will control the state of the system X t such that this performance index is minimized not only that control input and state because control input state will satisfy this equation. That means this you find out the control input U in such a way this functional is minimized or maximized control input control problem is minimized let us call and then subject to this constraint and that constraint is the equality constraint. So, our problem is now becoming a what is called a constraint optimization problem and that constraint is equality constraints are there. So, I just write the statement of the problem objective find U of t whose dimension is m cross 1 number of input says m that means control law only that minimizes performance index P i means performance index. Let us call we just write this equation is equation number 2 agree that performance index 2 subject to plant dynamics subject to equation 1 plant dynamics system dynamics subject with this such that our problem is find a U only that minimized the performance index subject to the constraint that means whatever the control input we generate and x generate this must satisfy the equation number 1 that is a such in this type of problem is called such in problem optimal control problem is known as Bolgia problem. So, this is our problem now let us see if you look at this things what is difference from the earlier problem we have a same thing here earlier problem also we have to what is called integrand v is there we have to integrate 0 to 2 e f and that functional we have to minimize, but in addition to that there is another term is there which will called what is called is the terminal cost and that count physically represent the final state of the system agree and in terms of it quadratic form this and that quantity is must be a positive on that one. So, this I mean not only this there is another constraint is there it must satisfy this equality constraint and this equality constraint is nothing, but a what is called that dynamic equation of the system this equation is the dynamic equation of the systems. So, by some means if you can push it this term into the integral part of this equation that equation then our problem is similar to the earlier problem let us see this how one can do this one. So, note because our job is how to push this term into a integral part of this functional agree. So, now see this one we can write it now t 0 to t f d s x t which is function of time and d t we have just mentioned earlier that this is the continuous function which is differentiable with respect to x t as also t. So, this I can write it this into d t is nothing, but a that if you see this one this nothing, but a x of t comma t t is equal to t f minus x you can write it x t of t t is equal to t 0 which is nothing, but a x x t f t f minus x x t 0 and t 0. So, in place of this one I can write this term and this term. So, this limit is an integral limit of this one is same t 0 to t f. So, I can push it in equation number 2. So, if you push it is let us call this is equation number 3 agree using 3 in equation 2 using 3 in equation 2 what we get it just look at this expression that this is this minus this one I am using this one. So, if you do this one j of dot is equal to integration I am just keeping one step this v of x of t u of t then t d t that one plus t 0 to t f d s x of t t d t whole bracket d t plus s of x t 0 and t 0 this. And this is the constant term because you know that t is equal to t 0 what is that initial condition of this one you know this one this is the constant term. Now, our whole problem is now if you see our problem is now this one minimize this one in place of minimizing this one minimize this term let us call equation 4 agree this is equation number 2 3 and this is 4 minimize equation 4 is same as minimize equation number 2 agree minimize equation number 4 such that minimize in the you find the optimal value of control you such that this is minimize. And as well as this equation is satisfied since this is a constant term that optimal trajectory will remain same if you consider the minimization of this part only. So, instead of whole thing minimization this part minimization whatever the optimal trajectory you will get it agree for u transpose n x transpose that will minimize that as well as it will satisfy this one. So, we will stop it here next class we will continue this lecture in detail.


Welcome everybody to another episode of the hot pot boys. We got Nellie Nell Chan We got David and Andrew from the Fung Brothers today.  I'm super excited about the spot We have the Sino Soul series where we delve into provincial Chinese cuisines This is the very first episode of the modern Asian series For example the very first spot that we're going to be covering is pepper lunch That lunch is a chain from Tokyo and got popular all over Asia and now they're moving to America Finally we are getting the direct port from Tokyo fast-stake grill your own meats in Japan They love the sizzling hot plate steak, and I'm not saying it's traditional.  All right, so we are gonna be trying 12 different things here at pepper lunch I'm ready to go to Tokyo. Hop Hop boys. Let's go. Mix it. Who knows how to mix it? All right, you guys you spread it first I got the kimchi beef. This is one of the most popular ones The key is like the electromagnetic oven this guy invented the Electromagnetic oven to heat these pans up to keep your meal hot for 20 minutes. I watched some videos online About how to flip it now this one. This is the hamburger steak. I'm gonna flip this Like using chopsticks. I think it breaks up the rice easier All right, you guys let's all try the kimchi first. All right, this is the kimchi cheese That's the thing about having your own grill is that you know the food is piping hot I think the only worry that you got to think about is over cooking your meat, but this right here So it's called pepper lunch because they have lunch prices all day and the main seasoning for the meat is pepper The flavors here are not too crazy salt and pepper butter Some margarine they keep it simple It's kind of similar to like your kimchi fried rice in a sense, but a lot cheesier. Yeah, okay So this is the jumbo pepper rice. This one is actually a lot more peppery. This is good This has a much stronger pepper flavor. Yeah, it does so this sauce that you have here on the table is the honey soy sauce Okay, so that's gonna be like a sweet soy sauce and then this one is your garlic soy sauce I like the strong pepper flavor the way they made it right here for the jumbo beef I give it a 4.5 out of 5.  Yeah, mm-hmm of the first round. I still think the jumbo beef was the best one This is number one just because this almost had too much cheese. I almost got to go with one two three My number one I'm gonna go with the jumbo slice too. Okay second I'm gonna have to go with the kimchi the kimchi flavor is this really really pop it one two three for me easy boom The kimchi had more punch and to be honest. I'm not a huge fan of Hamburg steak We got to do this handle this steak the steaks came in hot you can easily overcook your steak But here's how you don't bread the butter on top Nelson. I'm going to hurry. No, it's exciting. It's only a matter of time You can't over cook it. Okay. Okay.  Okay, so flip each day You know you guys I've got the wild angus Wow It's snowing you don't want it to cook anymore. Then you put the steak onto the veggies Yeah, so you are creating a layer on top of your grill Nelson right now See those to it right right on top right on the carrot. You have the rib eye here. I'll give you the meatiest piece Pause rib eye. No sauce. No sauce But then a good job. No get the rib eye, but don't cook it that much. Okay this though Look at that grill mark bro. That's real. That's a real grill mark New York strip Look at my piece right here. You still got a little red in the middle strong steak beefy flavor A lot more chewy more like the steak that you might cook at home Or that is when you want to feel like a carnivore Look at that. Wow, this is a big piece Technically should be the chewy is wild angus chuck. I love the amount of David the garlic flakes on there. It smells good Okay, great flavor, but a little chewy. You're gonna have to bust out the knife for this one All right guys. This was the steak round We had rib eye. We had new york. We had chuck. I think the best slice Of this chuck was better than the best slice of this new york strip one two three I'm gonna go with rib eye New york and the chuck. I'm gonna go with the new york number one. Wow Because I thought I had the most pure steak flavor to me.  It's kind of like an individual hot pot where you got to watch over your stuff You are responsible.  You're gonna help us judge this round Okay, okay Okay, that was the kale spinach pasta Seafood cream pasta. Okay. Oh man. They're flying in. It's getting a little crazy. I've had for lunch right now I put it on Flip the camera over here. What are we doing? David? Yo, how do I cook this? Yo, we need spoons. Hold up We don't have the tools. Nobody gave us the tools David David, I believe in you We're winning. We're winning. Do the walk work. Do the walk work We're right now. Pepper lunches. We're not just open. I've actually never seen them like Make their boom I don't know how I feel right now Kirsten was walking on the street kirsten you passed by us while filming and I was like, yo Kirsten always wanted to get you in the video. Get in the video Tell me kirsten again Kirsten. Yes, Andrea Shouts. Okay, so I do like how the mushroom it is grilled on one side. I got a piece of salmon There's scallops salmon and mushrooms in this. All right guys seafood cream pasta All up in this She's an eater So what I liked about the noodles was that that part of them was browned and a little bit crispy on some of the sides I actually like the cream sauce a lot. I don't like it was a very very light Afraid of white sauce these japanese pasta dishes are always kind of like It's like italian food for people who are not trying to get the authentic italian food. Let me review this one for y'all Okay, this seafood as creamy as pasta got salmon scallops mushroom and shrimp inside a cream sauce Let me tell y'all when you eat the pasta it is all flavored throughout. It is so yummy It's just the right amount of like creamy buttery cheesy smoothness in there So that's how this one tastes it tastes delicious a 10 out of 10 Welcome to He's coming around. Oh wait, this is the right order. Razzie like all this Just look at the mint basil. Let's move on. Let's move on. Let's move on guys This is the kale and mushroom cream pasta. We're gonna try this right now kale spinach pasta That's actually really good. Oh, there's not a lot of flavor but the flavor that it did have It almost tasted it almost tasted like a pesto. I think it tastes more fresh Than um the other pasta than the seafood one. There's it's more like simple flavors like the kale and the spinach So this is more milder pasta All right international citizens, please please. All right, this is the seafood. What is this people are right seafood rice I taste that soy sauce. I taste that butter. Y'all put a lot of butter in here because I taste it I'm from Georgia. I know what butter tastes like. I think that this is really one of the most fun lunch experiences that I've had in several months I think as technology moves forward and everybody is on their phones As people are on their phones more and more and having less human to human interactions I think stuff like this is important because it causes a ping in an interaction with each other between the seafood cream pasta the kale The kale spinach pasta with no meat and then the seafood rice. What are you going with for your top two? Seafood pasta kale pasta seafood rice. Did you guys say hi to a favorite? Kirsten Kirsten is a celebrity Anyways, okay, we have our last round Which is we're eating our salmon filet. We have our beef right here and then we have our actual steak salad All right in terms of what won out I think you got to go for your money with the jumbo pepper rice My favorite overall if I had to recommend you get one thing Jumbo pepper rice because that is like the iconic dish that really makes pepper lunch pepper lunch I'm going with jumbo rice steak and then the kale is so when I was living in japan I actually came to pepper lunch to eat the humbug steak. We're editing in english right there Sometimes y'all got editing skills and stuff and I know that y'all gonna insert it right here Well, what's it like to see modern chains from your time you were living in japan and see it come to america? You know one thing I realize is that like for some of the more traditional food It's almost unlikely that it's gonna be elevated to a point where the younger generation wants to be a part of it I know some people are like it make a traditional or nothing at all and I'm like no guys It's all good. Like, you know, this is a modern chain from japan And it's finally porting itself to the u.s with a few slight changes Well, I think even spots like this are just expanding the definition of what is asian food You're seeing a steak a ribeye steak. You're like, oh, that's not really asian Well, this is like an asian way of cooking it from asia This was a dope first episode for the first episode of the modern asian series for hot pot boys Thank you kirstin for joining us All right, everybody. Thank you so much for watching that video. Thank you to kirstin for coming by Nelson we're gonna have pepper lunch. All right, everybody in the comments below Let us know what other modern asian spots around the area We should check out and do a hot pot boys video at and also let us know what you think about the modern asian spots Versus the traditional spots, you know, because they are pretty different And I don't know if you can go to all of them because not everybody has all the time in the world So you definitely got to pick and choose but asian food is is huge now I don't know. It's hard to say But anyways, let us know in the comments below. Let us know what your thoughts are Um, you can check out all our instagrams down below and until next time we out. Peace Joe was going on everybody. Thank you so much for watching that video Uh, basically we are gonna be releasing a lot more content that we always wanted to give you guys We never really had a good way of doing it And that's why we want to tell you guys that we are starting youtube memberships So basically if you subscribe to the membership channel, you are gonna get tons of exclusive content You're gonna get exclusive photos exclusive videos We're gonna be doing mba talks comments on comments. You're gonna be getting merch discounts Basically, you can just click the join button right there It is only 4.99 per month and it's gonna go all on our community tab right here So it's exclusive content that you're only gonna see if you're a member But I think I think you might really like it. Yeah, we're gonna be delving deep into a lot of topics And we got some thoughts man. Yeah deep thoughts. So it's starting on january 30th So go ahead. Please uh sign up today and check it out. All right, everybody. Thanks for watching that video until next time. We out. Peace


Good morning guys and welcome to vlogmas day two right now. I just got up. It's about eight o'clock I love sleeping in but I can't sleep in too too late because I get up so early for school that like It doesn't really work out me sleeping in like later than nine But right now I am working on vlogmas day What day is this? I've like organized everything so it'll just be easier like I'm not deleting anything So I have like my music like all the Christmas music imported I have my graphics up there like the intro and outro and stuff and then I have a footage area This one's gonna be like super short. Sorry But it was a school day. That's why it's short. So I have graphics and music and then footage We are on vlogmas day tail. So this is vlogmas day three. I think I just said that I don't know guys on the camera today. I love logging with the camera. It's so much Well, it's not better It's just different than my phone So I'm gonna quickly edit this schedule it get it up And then I'm going to throw in a little towels already mentioned in the video. I'm editing Well, I'm gonna say to kind of like my game plan for today.  I think that would be so fun If I like threw parties or whatever like I have so many like games and activities I would play like I would do gingerbread house contest Where everyone like if you wanted to participate like would give me like I don't know what 10 books to get Gingerbread house at like dollar store or whatever and then we did do that and then I was telling my friend Like a drunk jewelry making Activity would just be like so fun I don't know you play like a drinking game and then you'd like draw out of a hat who you would be making like a Jewelry piece for like, you know, the beaded ones, you know the beaded ones You can get it like Claire's and stuff They're like in well, you can just totally make that just go to Michaels or Joanne's and Make it but I think it'd be fun like for a party. I don't know. I'm giving away all my secrets But if you want to steal any by all means But I'm gonna finish this and we'll see you where the day takes us. Okay, I'm back But I just made a really impulse purchase which is not that good, but God I had to get this Okay, so I don't know if you guys know this but I got this blanket and I really should be editing right now But I saw Karen's Instagram story and I was like, oh my gosh, I have to have it So, you know this blanket that I got This one we keep it down here because it is so soft It's so nice to have near the couch. We always use this blanket It's like right over there It matches our house that this one doesn't really match because it's like this taupe color So this blanket is the softest blanket ever. I'm obsessed with it It's the best $100 I spent other than my Stanley cup Which is like a great piece to that like I am obsessed with right now I carry it like literally every day ask anyone but anyway, you know this blanket the softest thing ever small business a family owns and I like shopping small to support small Businesses and creators and everything best blanket in this entire world guys There's a robe made out of that same material and don't get me wrong like I love this one This one's from the Riviera my favorite Disney resort or the Riviera is my favorite, but This one's gonna be like probably more for like travel and stuff I don't know But I am so obsessed with that blanket and they make it in Robe form. Can you imagine like wearing that blanket as a robe? So I just bought it Christmas present to myself. Don't really need it when I want something I know I want something and it's not like a thousand dollars I just buy it for myself or I should say like $500. I buy it for myself.  It's probably due to inflation, but anyway now I'm for real I'm gonna start editing. All right, so got dressed and this is my outfit Wanted to keep it casual today because today is a casual day I think I'm gonna head out now and we're gonna just do some holiday shopping. So Stay tuned We made it to Target and Let's see what they have It is starting to look like Christmas in here guys. Oh my gosh. Here's the gingerbread houses These are $15, but I think I'm gonna do the ones that they like come with everything So, oh hey, here we go. So we have The little letters to Santa we have the gingerbread house. We have a pink one and Then we have like this one on a tree trunk, which is pretty cool I think I did that one last year with the three houses So look, there's a mini village a mini village. Okay Anyway, I think I'm gonna do this one Just because it's like more traditional 13 bucks for the gingerbread house Not bad. Not bad. Also guys. Look at how cute. I cannot wait to have. Oh my gosh. I Just bumped that. Okay. Anyway, what I was saying was I cannot wait to have little families have matching pajamas with Well, this is a robe, but still you guys get the point.    I don't know so I haven't really decided Officially I see the Christmas stuff guys. How exciting Okay, so this is the hardest part getting a thumbnail So I'm just going to wait for these people and then we're gonna get a thumbnail I think the mission has been accomplished. Okay, so I already see a couple of bags that I Think I might get for my classmates because they're pretty tiny. I mean the pouch isn't that big So I don't think no huge bag is necessary, but for my other friends.  Okay, so I went with this tissue paper because it'll match.  They come with two bags, right? So I'm getting Through my classmates something and then our teacher a little something so Four is actually saying go for my camera died So I'm gonna get four because I just have four people that I'm giving gifts to and then this bag This one my friend because her gift is like kind of larger. I don't know if it'll fit in here But I can always put it like slanted, you know, I Don't know I might need to get another bag. Okay, so I actually decided I'm just gonna get this one because when you open Up, I can just push it down in there. I don't know. I think this one's cute. So I'm gonna get that one but look how pretty all of the Christmas stuff at the front is right now I'm looking for a Christmas card and there's more bags over here, too But I want to get a Christmas card for everybody. So this is always a hunt It always takes me so long to pick out Christmas cards for people like I don't know I'm just gonna keep a general for my classmates, but like for my friend like, I don't know It's hard always hard. Okay, so I've made the executive decision on this one and it comes with eight So everyone I'm getting a gift for is gonna get the same part It's a lot easier to just have the same part. So That's checked off the list. All right, so I picked up a few more things. This is for my parents anniversary and it actually says Celebrating two amazing women. Oh my gosh. We've come so far as a society And then I got Some gift cards for my classmates. I want a target because like it's kind of general and you can buy whatever you want So I'm gonna get some gift cards. This is for one of my classmates as well I know she likes Starbucks. So that's the only reason why I got her that one, but okay So mission has been complete. I got all my goodies. They're not all mine. They're for people But the lady that was like checking people out one of them I swear first of all target should hire like more check out people and they pay like $15 an hour, which is like a good Like substantial wage, but like I swear that there's they need to hire more people because The self-checkout is taking away jobs, you know what I'm saying? So like and half the time people don't even know how to work the machinery So people are just standing there with their arms up and then like the person already has to go and help them So you might as well just have more people so you can get people through the line more But the lady she was like not the friendliest. So I'm like, okay, but whatever. Maybe she's having a bad day It's fine. But now I think I'm going to get some chick-fil-a. I was in the Starbucks line I'm like, you know what? I haven't had chick-fil-a in a while. So I'm gonna have some chick-fil-a I know the line's gonna be long. So it's fine. It's like noon right now fine old time out Well, and then I'm gonna run into Publix, which I'm not gonna like vlog because there's like two things I need so Three I'm think I'm gonna get some lettuce And a green pepper And then I need laundry detergent like that's the main reason why I'm going because I'm doing laundry today And we don't have any left so that is the game plan for Publix But it's like a quick trip in and out. This was such a vlog fail. I just finished my nuggets I realized I didn't vlog. But anyway pretend there's chicken nuggets in here. Here are the fries. Oh my gosh I was so hungry. I didn't realize how hungry I was but Got the chick-fil-a. Okay, so I just got home and I have to put some of the groceries away But look, this is the wedding invitation for one of my shaman sisters. Oh my gosh, how cute This is adorable, I don't know if they like want me to show it or not, but I'm opening it up And I think it's adorable. So it's just like a picture of them with a truck pretty much Made myself some coffee because I didn't end up going to Starbucks, but I still wanted coffee today It's my compromise. I got chick-fil-a, but I'll have coffee from home all about bounce all about Compromise so I just asked Instagram and I wanted to ask you guys leave in the comments down below I see everyone dyeing their hair darker Should I just like go back to black? Should I keep this? I'm gonna get the curtain bangs I know someone commented like saying oh don't get them or whatever But the thing is it's like it's just bangs if I don't like it The bangs will just grow out eventually and I've had bangs before like when I was younger So like if I really don't like them or they just don't turn out the way I want them to It's fine because it'll grow back I like trying new things with the hair as you guys will know you should know that by now Like I cut my hair on camera.  So I am Going to sip on this and I'm going to start the movie I don't know if I'll put Christmas ornaments on the tree I might work on like one box while I watch the movie or might just like watch the movie But I have a laundry going and everything like that I wrote in all of the Christmas cards that I'm going to give to my classmates and friends. So Yeah, that's pretty much what I've done And yeah, it's a really good Saturday. It's like a good self-day self-care Not really self-care, but like it's a good buy myself Saturday. Honestly too guys I think I'm gonna change cuz like this is not a comfy outfit as you guys know Like I live in oversized t-shirts with no bra and no pants because it's just the life That's like so comfortable and I'm home. So why not probably next time I go upstairs I'll put on my comfortable outfit. All right, so I'm on well Okay, you just switch but I'm almost done with the series. I think there's like eight episodes So I'm on six, but it's so good, but I'm gonna eat now. Sherry is bringing home some Panera I ordered a small mac and cheese and hopefully like one of those seasonal iced cookies because they're so good and with that I'm gonna have a salad just cuz you know me and I got the stuff today. So why not? I did have a candy cane though. I Don't know if I showed you guys this but Valerie got candy canes and I Ate one today my first candy cane of the season and some mac and cheese. Okay, so it's the next day I did not finish watching the Series like the acting one not the documentary one. I have two more to go. I don't know what I'm gonna actually finish it Just because my parents got home we ate and then we watched an episode of dead to me So I didn't end up getting to finish it, but that's okay Right now. I'm just like I said in doing this video so I can edit right now If you guys enjoyed it, make sure you give it a thumbs up Don't forget to subscribe and I'll see you guys in my next video. Bye


Why we must stop hailing politicians? A politician builds a makeshift wooden bridge across a wide gutter and invites dignitaries to a fanfare to commission the contraption. Probably erects a signboard there with his name boldly on it. Splashes pictures on social media. I have not submitted anyone honestly. We applaud, we hail the politician because we remember suddenly that there has not been a project like this in the area for 50 years. This is the first we say conveniently, forgetting that this is the year 2021. The former students of a public school put funds together to build a toilet for the school. They invite the commissioner or permanent secretary of the Ministry of Education in the state to commission it. The government official shows up probably to cut the tape of the toilets in the school that they are paid by us to run but that has now ended up having a basic but compulsory facility such as a toilet built by private citizens. The people who pay for the toilet hail the commissioner for taking time out of their busy schedule to attend. I have concluded that there is something seriously wrong with the Nigerian public office holder. But the disease is not half as bad as that which is plaguing the Nigerian people. Yes, the suffering masses. We complain about how hard and bad things are on a daily basis. Yet when the time comes to take a stand, we are the chorus leaders and the applause commanders. We just love it. It is almost as if it is part of some custom or tradition to show gratitude to ineffective public office holders. It is as if we disagree. The public officials or us and by us I mean their bosses. Yes, we are the bosses. The citizens value for our money. These people actually also want to own us. We want to disregard almost on a per second basis. Our politicians in Nigeria are some of the highest paid in the world and I mean legally and illegally. Yet when they embezzle billions of Naira and give us of standard roads, bridges and other infrastructure, captains of industry and traditional leaders will line up to sing their praises. Now let me take you somewhere else to the UK where the UK government spent an estimated 500 billion pounds just to support UK citizens during the COVID-19 pandemic. The UK Prime Minister Boris Johnson. In fact, all they have done is question his methods, policies and preparedness. Whereas Johnson rides in a two car convoy, nobody claps for that. He sometimes goes to work or about his duties in public transport, nobody claps. Roads are built and commissioned without fanfare, no foundation lanes ceremony or ground breaking, nobody claps. Now imagine this was Nigeria. One would begin to think the people who live in these countries are absolutely heartless or ungrateful. But there is a simple reason they don't clap. It is because there is no reason to clap. Public servants are servants after all. In fact, I see them more as paid slaves. They are being funded by taxpayer funds to serve their masters, the people. So why should the masters clap for their servants when they do a job they are handsomely committed to do, not to talk of them drilling over the most mundane achievements? A governor awards the construction of a six-kilometer road to a contractor who is his friend or crony. At an exorbitant value, the contractor does a shabby job. But by the grace of God, God with small letters, just manages to complete the project. The governor and the contractor share the profit. But the masters who get a badly built road are the ones who organize praise and worship sessions for the governor for building a food park where an expressway should be. Nigeria is still way off the mark in terms of development, and this is not by accident. Public hospitals and schools and ISO, institutions of deep shame, I call them. This hailing of public officials has to stop today. Absolutely. Well, I don't even know what to say. I don't know why. Let's take a minute to take it off. Why was the commissioner there to cut ribbon for toilets? There's no need for you to be there. Why did we invite him? Yes, someone invited him. For toilets or for cutting a ribbon for a window. At a local government office. Or a wooden bridge. The wooden bridge. I think it's a fundamental problem. We don't understand the meaning of the word service. Or servant. I don't want to say servant. If they say servant, they won't show. If they say public servant, they won't show. The word service is derived from word serve. And to serve means to be the servant. It brings you back to the word servant. If you understood that fundamentally. That this person is here to serve me. Then it changes the game instantly. But for us it's more of a game of... I'm here to help you. It's nothing we're talking about. I've built a road. I have a right to put a billboard. And then say road constructed by. Sir, it's what you're paid to do. By the way, it's public service. Even if you're not paid enough, that's the whole point. But I think it goes back to why people go into politics. It's not to serve. It's not here. It's not to serve. Because they know that structurally it's made to go and make money. That's why you go and make your money, go and make your name. You're not there to serve. You're not there to do good. You're there to enrich yourself and your cronies. So we also need to understand that. That is actually the lay of the line. It's great to say we're meant to be public servants, public service. But let's look at the reality on ground. That's not how it's looked and perceived as. Right? General public perceives it as his excellency. Her excellency. Excellency of course. I really despise having to say his excellency. What have you done that is excellence? What is excellence about? What do you see? OK, you go. OK, I would say that if you go to some local governments where you young youth core members serve, you hear about some youth core members who build bridges using their own allow as they use their 23,500. I don't know what they are paid now. But they use something that's little to build bridges to offer free medical care. So you are wondering. So why do we have leaders? Exactly. And there's a governor in that state and there's a counsellor in that state. Exactly. And those people earn more money. But I want to look at it from this angle. someone said he said the governor is so ready to work he cares about you hello this is an applauding not even on mediocrity i think you have been very kind the applauding of everything is so outstanding as long as it is finished he doesn't even need to finish so many uncompleted ఉఒ్ఽికాలొా. శిఆక్డిఙాటు-ధటినంట్లూ, న్లోటికిమ్endas81ంటలారెacağım యారెడిటకారомуరతుచ్తరకిక్పుఢుులె� నోర్ర్ను నీనునాలు gonna be on it. న్ర్చొనిందా న్చిపాసిల్త్స్ందాలికొికడిసికందుట్కుల్ట్ల్