Given the following system x (k + 1) = Gx (k) + Hu (k) G = [1 1 10], H = [1 0], x (0) = [1 0] Hand-calculate and Determine the optimal control sequence u (k) that will minimize the following performance index: J = 1/2 x^T (8) Sx (8) + 1/2 sigma^7 _k = 0 (x^T (k) Q x (k) + u^T (k) Ru (k)) where Q = [1 0 0 1], R = 1, s = [1 0 0 1] What is the minimum value of J? Program a MATLAB file to verify your hand-calculated results. Given the following system x (k + 1) = Gx (k) + Hu (k) G = [1 1 10], H = [1 0], x (0) = [1 0] Hand-calculate and Determine the optimal control sequence u (k) that will minimize the following performance index: J = 1/2 x^T (8) Sx (8) + 1/2 sigma^7 _k = 0 (x^T (k) Q x (k) + u^T (k) Ru (k)) where Q = [1 0 0 1], R = 1, s = [1 0 0 1] What is the minimum value of J? Program a MATLAB file to verify your hand-calculated results