Given the following system x(k + 1) = Gx(k) + Hu(k) G = 41 11. ) H = (0) = [%] (a) Hand-calculate and Determine the optimal control sequence u(k) that will minimize the following performance index: 1 J = x (8) Sx (8) + (x (k)Qx(k) + (k) Ru(k)) k=0 where LO Q = [1], R R = 1, S = = (1 9 (b) What is the minimum value of J? Program a Matlab file to verify your hand-calculated results.