If the plant has cost index: where S(T) = S(T) = [ [010].e=[9] Q= 0 *-...

 

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If the plant has cost index: where S(T) = S(T) = [ [010].e=[²₂9] Q= 0 *- J*+- = x+ 0 1 J(t)= 1⁄2x(T)² S(T)x(T) + ½ [[[x²¹Qx+u² Ru]dt 2 to 20 U R = 2, and final time T = 20. The state variable at the initial 3 condition is x (to) =| . At the final time, the state must satisfy the following equation: y(x(T),T)=Cx(T)-r(T)=0 where C = [1 0], r(t) is an analytical function of t. It means that the state must track the reference r(t) at the final time. (a) Using MATLAB simulation to find the optimal tracking control to track the reference r(t) =t², please plot the control u(t) and x(t), r(t) versus time; (b) Using MATLAB simulation to find the optimal tracking control to track the reference r(t) = cos(t), please plot the control u(t) and x(t), r(t) versus time. If the plant has cost index: where S(T) = S(T) = [ [010].e=[²₂9] Q= 0 *- J*+- = x+ 0 1 J(t)= 1⁄2x(T)² S(T)x(T) + ½ [[[x²¹Qx+u² Ru]dt 2 to 20 U R = 2, and final time T = 20. The state variable at the initial 3 condition is x (to) =| . At the final time, the state must satisfy the following equation: y(x(T),T)=Cx(T)-r(T)=0 where C = [1 0], r(t) is an analytical function of t. It means that the state must track the reference r(t) at the final time. (a) Using MATLAB simulation to find the optimal tracking control to track the reference r(t) =t², please plot the control u(t) and x(t), r(t) versus time; (b) Using MATLAB simulation to find the optimal tracking control to track the reference r(t) = cos(t), please plot the control u(t) and x(t), r(t) versus time.

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Below are MATLAB code snippets for solving the optimal control problem for both reference signals rt ... View the full answer