An Inverse Problem of Optimal Regulator

Abstract

An inverse problem of the optimal regulator is considered for a class of multi-input systems described in a new canonical form. Due to a compact structure of the systems, the analyses are conveniently performed to get relevant characteristics of optimal control systems. Necessary and sufficient conditions for optimized performance indices are given. Assumed that nonlinearities of the system exist only in the part of the directly controlled state variables, a further investigation is directed to the nonnegative property of optimized loss function. In the context, two major topics are considered. One is concerned with a question, “What performance indices can be optimized by identically zero feedback control law?” The other is “What performance indices can be optimized in a linearly synthesized feedback control system?” As an arbitrary system can be transformed into the canonical form, the assumption about the system structure does not restrict the applicability of the results obtained in this paper to general problems.