Numerical Solutions of Hereditary Control Problems via an Approximation Technique.

摘要

This report discusses in some detail, numerical results for certain hereditary optimal control problems. The numerical procedures involved are based on the approximation ideas proposed by Banks and Burns. The resulting method is easy to implement and in most cases the convergence of approximate solutions to the actual solutions is quite good. Attention here is restricted to control problems with quadratic payoffs. (Somewhat more general payoffs and linear systems could have been treated.) The main reason for this is the case in demonstrating the computational feasibility of the method. Indeed, for the integral quadratic cost problem treated here the approximate control problem becomes a finite dimensional linear regulator problem which is easily solved numerically via standard techniques. In Section 2 a brief description of the problem and our method is given. Section 3 contains a number of examples which are solved exactly using the maximum principle, and in Section 4 representative numerical details for approximate solutions of these examples along with numerical results for several other examples are presented.