Linear Quadratic Control Problem With Fixed Final State for Discrete-Time Distributed Systems

Abstract

The problem considered is that of minimizing a quadratic cost functional for a discrete distributed system with fixed initial and final states. It is shown that under suitable controllability assumptions, there is a close relationship between this problem and that of exact controllability with minimization of a time-varying energy criterion. The HUM technique is then extended to treat the exact controllability problem in the time-varying case and applied to provide an explicit form for the optimal control and the optimal cost