H/sub ∞/ optimization with time-domain constraints

Abstract

Standard H/sub /spl infin// optimization cannot handle specifications or constraints on the time response of a closed-loop system exactly. In this paper, the problem of H/sub /spl infin// optimization subject to time-domain constraints over a finite horizon is considered. More specifically, given a set of fixed inputs w/sup i/, it is required to find a controller such that a closed-loop transfer matrix has an H/sub /spl infin//-norm less than one, and the time responses y/sup i/ to the signals w/sup i/ belong to some prespecified sets /spl Omega//sup i/. First, the one-block constrained H/sub /spl infin// optimal control problem is reduced to a finite dimensional, convex minimization problem and a standard H/sub /spl infin// optimization problem. Then, the general four-block H/sub /spl infin// optimal control problem is solved by reduction to the one-block case. The objective function is constructed via state-space methods, and some properties of H/sub /spl infin// optimal constrained controllers are given. It is shown how satisfaction of the constraints over a finite horizon can imply good behavior overall. An efficient computational procedure based on the ellipsoid algorithm is also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>