A highly computational efficient method to solve nonlinear optimal control problems

被引:6
作者
Jajarmi, A. [1 ]
Pariz, N. [1 ]
Kamyad, A. Vahidian [2 ]
Effati, S. [2 ]
机构
[1] Ferdowsi Univ Mashhad, Adv Control & Nonlinear Lab, Dept Elect Engn, Mashhad, Iran
[2] Ferdowsi Univ Mashhad, Dept Appl Math, Fac Math Sci, Mashhad, Iran
关键词
Nonlinear optimal control problem; Pontryagin's maximum principle; Two-point boundary value problem; Optimal homotopy perturbation method; Suboptimal control; HOMOTOPY-PERTURBATION METHOD; DIFFERENTIAL-EQUATIONS; SYSTEMS;
D O I
10.1016/j.scient.2011.08.029
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, a new analytical technique, called the Optimal Homotopy Perturbation Method (OHPM), is suggested to solve a class of nonlinear Optimal Control Problems (OCP's). Applying the OHPM to a nonlinear OCP, the nonlinear Two-Point Boundary Value Problem (TPBVP), derived from the Pontryagin's maximum principle, is transformed into a sequence of linear time-invariant TPBVP's. Solving the latter problems in a recursive manner provides the optimal trajectory and the optimal control law, in the form of rapid convergent series. Furthermore, the convergence of obtained series is controlled through a number of auxiliary functions involving a number of constants, which are optimally determined. In this study, an efficient algorithm is also presented, which has low computational complexity and fast convergence rate. Just a few iterations are required to find a suboptimal trajectory-control pair for the nonlinear OCP. The results not only demonstrate the efficiency, simplicity and high accuracy of the suggested approach, but also indicate its effectiveness in practical use. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.
引用
收藏
页码:759 / 766
页数:8
相关论文
共 50 条
[31]   Multistage Linear Gauss Pseudospectral Method for Piecewise Continuous Nonlinear Optimal Control Problems [J].
Li, Yang ;
Chen, Wanchun ;
Yang, Liang .
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 2021, 57 (04) :2298-2310
[32]   Heat-Equation-Based Smoothing Homotopy Method for Nonlinear Optimal Control Problems [J].
Pan, Binfeng ;
Ran, Yunting ;
Qing, Wenjie ;
Zhao, Mengxin .
JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 2025, 48 (02) :297-310
[33]   On homotopy analysis method applied to linear optimal control problems [J].
Zahedi, Moosarreza Shamsyeh ;
Nik, Hassan Saberi .
APPLIED MATHEMATICAL MODELLING, 2013, 37 (23) :9617-9629
[34]   The geometry of the solution set of nonlinear optimal control problems [J].
Osinga, Hinke M. ;
Hauser, John .
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2006, 18 (04) :881-900
[35]   Turnpike in Nonlinear Optimal Control Problems With Indefinite Hamiltonian [J].
Lu, Yi ;
Guglielmi, Roberto .
IEEE CONTROL SYSTEMS LETTERS, 2024, 8 :2691-2696
[36]   The Geometry of the Solution Set of Nonlinear Optimal Control Problems [J].
Hinke M. Osinga ;
John Hauser .
Journal of Dynamics and Differential Equations, 2006, 18 :881-900
[37]   Convergence of solutions to nonlinear nonconvex optimal control problems [J].
Anh, Lam Quoc ;
Tai, Vo Thanh ;
Tam, Tran Ngoc .
OPTIMIZATION, 2024, 73 (13) :3859-3897
[38]   OPTIMAL HOMOTOPY PERTURBATION METHOD FOR NONLINEAR PROBLEMS WITH APPLICATIONS [J].
Marinca, Vasile ;
Ene, Remus-Daniel ;
Marinca, Bogdan .
APPLIED AND COMPUTATIONAL MATHEMATICS, 2022, 21 (02) :123-136
[39]   Solving a class of linear and non-linear optimal control problems by homotopy perturbation method [J].
Effati, S. ;
Nik, H. Saberi .
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2011, 28 (04) :539-553
[40]   ANALYTIC-APPROXIMATE SOLUTION FOR A CLASS OF NONLINEAR OPTIMAL CONTROL PROBLEMS BY HOMOTOPY ANALYSIS METHOD [J].
Effati, Sohrab ;
Nik, Hassan Saberi ;
Shirazian, Mohammad .
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2013, 6 (02)