OPTIMAL-CONTROL OF A CLASS OF TIME-DELAYED DISTRIBUTED SYSTEMS BY ORTHOGONAL FUNCTIONS

A class of optimal control problems for multi-dimensional structures d escribed by a linear partial differential-difference equation is consi dered. The control mechanism involves the simultaneous application of time-delayed feedback and open-loop controllers which provides an effe ctive means of suppressing vibrations in the structures. A computation ally attractive method for determining the optimal open-loop control o f an optimization time-delay problem with quadratic performance index is presented. The method is based on using finite orthogonal expansion s to approximate state and open-loop control variables. The representa tion leads to a system of linear algebraic equations in terms of feedb ack parameters as the necessary condition of optimality. This method p rovides a straightforward and convenient approach for digital computat ion. Thus the difficulty in obtaining the solution of the coupled init ial-boundary-terminal-value problem with both delayed and advanced arg uments, which is always required in applying the Pontryagin's maximum principle to optimization of delay systems, is avoided. The unknown fe edback parameters are numerically evaluated from the solution of the e nergy minimization problem. A numerical example is given to demonstrat e the applicability and effectiveness of the proposed method. (C) 1998 The Franklin Institute. Published by Elsevier Science Ltd.