Optimal Projection Equations for Finite-Dimensional Fixed-Order H2-Optimal Control of Infinite-Dimensional Discrete-Time Systems

摘要

In the paper the authors are concerned with the fixed, finite-order H(sup 2)-optimal control of linear, infinite dimensional discrete-time systems. The set of necessary conditions for the existence of the H(sup 2)-optimal controller is expressed in terms of four operator equations (two modified Riccati equations and two modified Lyapunov equations) coupled by a projector having the rank given by the dimension of the compensator state. It is shown that, when the order of the compensator is equal to the order of the plant, the four operator equations are decoupled and the authors obtain the infinite-dimensional generalization of the finite state-space solution to the H(sup 2)-optimal control problem for time-varying systems as given in a 1992 paper by Ionescu and Weiss. (Copyright (c) 1993 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)