Sensitivity theory application to the numerical solutions of the general optimal control problem

Abstract

This study proposes various efficient numerical methods for the general optimal control problem. The basic feature of the methods developed here is that they somehow exploit the ideas and the concepts of the sensitivity theory. First, a new method for solving TPBVP, which is met in seeking an open-loop solution for optimal control problems, is developed. This method can be briefly expressed as an iterative procedure which is based on trajectory sensitivities with respect to initial conditions. In the second part of the study, various numerical methods are developed for the closed-lobp solutions of general optimal control problems using performance index sensitivity functions with respect to controller parameters. These new methods may be treated in two categories : 1) Apriori polynomial approximation methods; Here the basic assumption is that controller parameter function is assumed to be formed by a polynomial function. 2) Aposteriori polynomial approximation method; In this method a sequence of subproblems are created using some intrinsic properties of the previous method. The values of the results of the subproblems are then used in the formation of the optimum controller parameter function.