Insensitivity of Optimal Linear Control Systems to Persistent Changes in Parameters

ABSTRACT Previous work on the sensitivity of optimal linear control systems [xdot] = Ax + Bu with quadratic performance index has concentrated on the effects of small changes in parameters. It is shown in this paper that the optimal feedback law u = − Dx is insensitive to (i.e. is unaltered by) a wide variety of persistent changes in A and B. Some explicit expressions for these variations in A and B are presented, including the cases when B is fixed, and when the change in A is known. If A is fixed any change in B results in a change in D, so that the system is more sensitive to changes in B than in A.