To account for the expenditure of energy and resources, the control signal is often included in the

Question:

To account for the expenditure of energy and resources, the control signal is often included in the performance integral. Then the operation will not involve an unlimited control signal u{t). One suitable performance index, which includes the effect of the magnitude of the control signal, is

(a) Repeat Problem PI 1.1 for the performance index.
(b) If A = 2, obtain the value of k that minimizes the performance index. Calculate the resulting minimum value of/.