A Solution of Covariant System for Nonlinear Optimal Control System

This paper is concerned with the solution of the optimal control for the nonlinear systems described by the functional expansions. When we solve the optimal control problem by means of Maximal Principle, the problem is reduced to the two point boundary value problem. As we remark that covariant vector is considerd as the function of state vector, we expand covariant vector as state vector to solve the two point boundary value ploblem. Then, using of analytic continuation, We try to extend the applicable region of this method. When the control time is infinity, the optimal control law is timeinvariant, and can be obtained easily in this case. Finally, we verify the validity of this method by the numerical examples.