A numerical method for solving optimal control problems via Legendre polynomials

Abstract

Purpose The purpose of this paper is to propose an iterative Legendre technique to deal with a continuous optimal control problem (OCP). Design/methodology/approach For the system in the considered problem, the control variable is a function of the state variables and their derivatives. State variables in the problem are approximated by Legendre expansions as functions of time t. A constant matrix is given to express the derivatives of state variables. Therefore, control variables can be described as functions of time t. After that, the OCP is converted to an unconstrained optimization problem whose decision variables are the unknown coefficients in the Legendre expansions. Findings The convergence of the proposed algorithm is proved. Experimental results, which contain the controlled Duffing oscillator problem demonstrate that the proposed technique is faster than existing methods. Originality/value Experimental results, which contained the controlled Duffing oscillator problem demonstrate that the proposed technique can be faster while securing exactness.