Optimal Damping of Forced Oscillations by Output Feedback

摘要

In this paper we consider optimal control by output feedback of a linear discrete-time system corrupted by an additive quasi-harmonic vector disturbance with known frequencies but unknown amplitudes and phases. The object is to design a robust optimal regulator which is universal in the sense that it does not depend on the unknown amplitudes and phases and is optimal for all choices of these values. We show that, under certain natural technical conditions, as optimal universal regulator (OUR) exists in some suitable class of linear or nonlinear stabilizing and realizable regulators, provided the dimension of the output is not smaller than the dimension of the quasi-harmonic disturbance. When this dimensionality condition is not satisfied, the existence of an OUR is not a generic property. We also show that any OUR for this (deterministic) problem is an optimal regulator for a class of stochastic control problems of similar structure.