SOLVE CLEARLY...

Find the optimal control input uc), OSIS, that minimizes the cost functional 1 (0)={[cz(t)=e(r)]}w[cx(+)-e(r)]++{[cx()-z6]} @[cx(1)26)]+d?()R4(e)} de *r Cx)" e where W 20, Q20, R>0, subject to the LTI dynamical system model XER *(t) = Ax (1) + Bu(t) x(0)=X ER" The cost function is designed to drive a function of the states z(t)=Cx(t) to track reference trajectories r(t)e R", OS1ST, while penalizing control effort. The optimal solution to the linear quadratic tracking problem was shown to be given by: u" (t)=-K (1)x(t)+R 'B' (1) K(C)=R'B'SO)