Analytical solution for a class of optimal control problems

The objective of this paper is to present a novel method to design a suboptimal controller for a wide class of nonlinear optimal control problems. The proposed method is a combination of a successive approximation method (SAM) and a Legendre pseudospectral method, for solving the extreme conditions derived by Ponteryagin’s maximum principle (PMP). An illustrative numerical example is included to demonstrate the accuracy, efficiency and the reliability of the proposed method.