A Two-Level Computing System for the Solution of Complex Optimal Control Problems

Abstract

This paper concerns the iterative computational method for solving a large-scale nonlinear optimal control problem. The system to be optimized in this paper is formed by interconnecting a number of nonlinear dynamical subsystems. Furthermore, some of coupling parameters are assumed to be "adjustable". This assumption gives rise to new feature.In order to circumvent the computational difficulties due to high dimensionality of the system a two-level computing algorithm for solution of the problem is proposed, where optimization is performed by interchanging the necessary information between the "center" (the second level) and a number of "processing units" (the first level).At the "center" the iterative algorithm of conjugate gradient method is carried out to obtain the solution, but the calculation of gradients is not carried out directly. It is partitioned into "processing units" of the first level, which are related to each subsystem, to reduce computational difficulties.The "center's" algorithm is illustrated by making use of logic flowcharts. A simple numerical example is presented to show the procedure of the present method, which will desirably be to be extensively used for the more complex version.