Given the plant of Problem 11.4-4, with the cost function

(a) Calculate the feedback gains required to minimize the cost function, using the difference-equation approach of Section 11.4.

(b) Find the maximum magnitude of u(k) as a function of x(0).

(c) Compare the maximum magnitude of u(k) in part (b) with the value in Problem 11.4-4(c). Explain the difference.

Problem 11.4-4

Given the first-order plant described by

(a) Calculate the feedback gains required to minimize the cost function, using the partial-differentiation procedure of Section 11.3.

(b) Repeat part (a) using the difference-equation approach of Section 11.4.

(c) Find the maximum magnitude of u(k) as a function of x(0).

3 J, = 2x2(k) k = 0