Solution of optimal control problems with Payoff term and fixed state endpoint by using Bezier polynomials

Abstract

In this paper, a new numerical method for solving the optimal control problems with payoff term or fixed state endpiont by quadratic performance index is presented. The method is based on Bezier polynomial. The properties of Bezier polynomials in any intervel as [a; b] are presented. The operational matrices of integration and derivative are utilized to reduce the solution of the optimal control problems to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Keywords

• Optimal control
• Bezier and Bernstein polynomial family
• Best approximating
• Operational matrices of derivative and integration
• payoff term
• Fixed state endpiont