H-INFINITY OPTIMIZATION WITH TIME-DOMAIN CONSTRAINTS

Standard H(infinity) optimization cannot handle specifications or cons traints on the time response of a closed-loop system exactly. In this paper, the problem of H(infinity) optimization subject to time-domain constraints over a finite horizon is considered. More specifically, gi ven a set of fixed inputs w(i), it is required to find a controller su ch that a closed-loop transfer matrix has an H(infinity)-norm less tha n one, and the time responses y(i) to the signals w(i) belong to some prespecified sets OMEGA(i). First, the one-block constrained H(infinit y) optimal control problem is reduced to a finite dimensional, convex minimization problem and a standard H(infinity) optimization problem. Then, the general four-block H(infinity) optimal control problem is so lved by reduction to the one-block case. The objective function is con structed via state-space methods, and some properties of H(infinity) o ptimal constrained controllers are given. It is shown how satisfaction of the constraints over a finite horizon can imply good behavior over all. An efficient computational procedure based on the ellipsoid algor ithm is also discussed.