IEEE Transactions on Automatic Control, Vol.39, No.4, 762-779, 1994
H-Infinity Optimization with Time-Domain Constraints
Standard H(infinity) optimization cannot handle specifications or constraints 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, given a set of fixed inputs w(i), it is required to find a controller such that a closed-loop transfer matrix has an H(infinity)-norm less than 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(infinity) 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 solved by reduction to the one-block case. The objective function is constructed via state-space methods, and some properties of H(infinity) 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.