A constrained optimal control of nonlinear systems

A new method for optimal control of nonlinear systems with input constraint is discussed in this paper. The system is optimized by minimizing a quadratic performance index. Considering this problem as a nonlinear programming problem, the necessary and sufficient conditions for optimal control are derived, which are later simplified to an integral equation. This integral equation becomes a necessary condition. The existence of a solution of this integral equation is studied, and a method of solving it is discussed. A numerical example is worked out at the end.