The first step in using the Hamilton-Jacobi-Bellman equation 0 = J*(x(t), t) + min {g(x(t), u(t), t) +JT(x(1), t)[a(x(1), u(t), t)]} a (t) is to determine the admissible control u*(?) [in terms of x(t), t, and J*] that minimizes { }. Find u*(t)-expressed as a function of x(t), t, and J-for the system (1) = x2(1) っ() = -x,() + x,() + u), and the performance measure J = [q1x}(t) + 92x3(1) + u*(1)] dt, 91, 92 > 0. The admissible controls are constrained by |u(t)|S1.

Q: T(1,1)=(5,0) Let T:²²be defined as, T(1,0)=(2,6) Then, T(3,2)=(12,6) (a) T(0,1)=(-3,6) (b)…

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Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

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Q: Assume that y, (1) = e and y, (1) = e" form a fundamental set of solutions. (b) Let y3 (t) = -4e2 Ya…

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Q: Define briefly u(t) and 8(t)

A: u(t): u(t) represents the unit step function, which is defined as u(t) = 0 for t < 0 and u(t) = 1…

Q: 13.Let x(1)(t)=(ettet),x(2)(t)=(1t).x1t=ettet,x2t=1t. Show that x(1)(t) and x(2)(t) are linearly…

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Q: independent solutions of y''+ P(x)y'+ Q(x)y = 0. Assume that f1(x) has at

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Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

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Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: Let f (x) C = C = = x on [0, 5], and let P = {0, c, 5}. Find two values of c in (0, 5) such that Uf…

A: Given function is  f(x)=x The partition P is {0, c, 5} We know that  Uf​(P)=∑i=1n​(Mi​)⋅Δxi​ Where…