Minimum trajectory sensitivity design of systems with random parameters†

Abstract

A method is presented for designing control systems with uncertain plant parameters and initial states. The open-loop part of a semi-closed loop control guarantees a proper behaviour under the most likely circumstances and a neighbouring feedback is augmented so that trajectory dispersion under random perturbation is minimized. It is shown that the resulting optimization problem is similar to the optimal regulator problem with incomplete state feedback. An original numerical method based on imbedding techniques is proposed to provide a suboptimal control which avoids solving a complicated two-point boundary-value problem. An example exhibits the trajectory sensitivity reduction achieved.