Optimal trajectory tracking based on perturbation theory of linear systems with feedback error

In this work we propose block processing based optimal stochastic control method for tracking a desired response with a closed loop system. We assume that the feedback system contains random errors which manifest as small random perturbations to the feedback transfer function. The approximate mean square trajectory tracking error is then computed by applying perturbation theory. This mean square error is minimized with respect to the operator input force and the non-random components of the feedback transfer function.