An iterative Legendre pseudospectral method for suboptimal control of nonlinear control affine systems

Abstract

The objective of this paper is to present a novel method to design a suboptimal controller for nonlinear control affine systems. The proposed method is a combination of a successive approximation method (SAM) and a Legendre pseudospectral method, for solving the extreme conditions derived from Pontryagin's maximum principle (PMP). The convergence theorem and the superlinear rate of convergence for this method are presented. Some numerical examples are included to demonstrate the accuracy, efficiency, and reliability of the proposed method.