Solution of Bang-Bang Optimal Control Problems by Using Bezier Polynomials

Yari, Ayatollah; Mirnia, Mirkamal; Heydari, Aghileh

Solution of Bang-Bang Optimal Control Problems by Using Bezier Polynomials

Document Type : Research Paper

Authors

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, Payame Noor University, PO BOX 19395-3697, Tehran, Iran

² Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz

³ Department of Applied Mathematics, Faculty of Mathematical Sciences, Payame Noor University, PO BOX 19395-3697, Tehran,Iran

Abstract

In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and conditions. Illustrative examples are included to demonstrate the validity and applicability of the method.

Keywords