PROBABILISTIC SENSITIVITY PROPERTIES OF NEIGHBORING OPTIMAL FEEDBACK SYSTEMS.

Recent results on sensitivity properties of feedback control systems when the initial state and plant parameters are probabilistic are reviewed and generalized. The feedback control law is assumed to be obtained from a quadratic optimization and linearized plant. It is shown that when a feedback control law is used, the trajectory is more likely to be near the nominal one when compared to open-loop control. The comparison is extended to a class of two feedback control laws with different weighting matrices in the quadratic index. The sensitivity properties are expressed in terms of likelihood ratios and volumes for sensitivity hypertubes which are also discussed.