A robust pseudospectral method for numerical solution of nonlinear optimal control problems

Abstract

In the present paper, a robust pseudospectral method for efficient numerical solution of nonlinear optimal control problems is presented. In the proposed method, at first, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality which are led to the Hamiltonian boundary value problem are derived. Then, utilizing a pseudospectral method for discretization, the nonlinear optimal control problem is converted to a system of nonlinear algebraic equations. However, the need to have a good initial guess may lead to a challenging problem for solving the obtained system of nonlinear equations. So, an optimization approach is introduced to simplify the need of a good initial guess. Numerical findings of some benchmark examples are presented at the end and computational features of the proposed method are reported.

Keywords:

• Optimal control
• Hamiltonian boundary value problem
• Pontryagin's minimum principle
• pseudospectral methods
• nonlinear programming problem

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49J15
• 34B15
• 65M70

Disclosure statement

No potential conflict of interest was reported by the author(s).