A numerical method for solving optimal control problems via Legendre polynomials. Issue 8 (31st March 2020)

• Record Type: Journal Article
• Authors: Gu, Yajing; Yan, Hongyan; Zhu, Yuanguo
• Is Part Of: Engineering computations. Volume 37:Issue 8(2020)
• Page Start: 2735
• Page End: 2759
• Publication Date: 2020-03-31
• Subjects: Optimal control -- Legendre polynomial -- State parametrisation; 49M30 -- 74H15; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-07-2019-0326
• Languages: English
• ISSNs: 0264-4401

Abstract

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.