A Numerical Approach to the Optimal Control Problem with Discontinuity

Abstract

Two numerical approaches, which are referred to as the solution methods I and II, to the optimal control problem with such discontinuity that the system has different system equations according to the regions in the state space are presented in this paper. In the solution method I, which has a character similar to that of the exterior point method, the criterion function is modified by adding some penalty function instead of using the condition that the system equation changes just at the boundary of the two regions. In the solution method II the condition of boundary is always satisfied in the course of iterative calculations. The theoretical relations between the solution methods I and II are also given.
The usefulness of the solution methods is illustrated by a numerical example.