If the plant has cost index: where S(T) = S(T) = [ [010].e=[9] Q= 0 *- J*+- = x+ 0 1 J(t)= 12x(T) S(T)x(T) + [[[xQx+u 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) =t, 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.