Solving a class of linear and non-linear optimal control problems by homotopy perturbation method

被引:30
作者
Effati, S. [1 ]
Nik, H. Saberi [1 ]
机构
[1] Ferdowsi Univ Mashhad, Dept Appl Math, Mashhad, Iran
关键词
homotopy perturbation method; optimal control problems; Pontryagin's maximum principle; Hamiltonian system; VARIATIONAL ITERATION METHOD; EQUATIONS; SYSTEMS;
D O I
10.1093/imamci/dnr018
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we give an analytical approximate solution for non-linear quadratic optimal control problems and optimal control of linear systems using the homotopy perturbation method (HPM). Applying the HPM, the non-linear two-point boundary-value problem (TPBVP) and linear systems, derived from the Pontryagin's maximum principle, are transformed into a sequence of linear time-invariant TPBVP's. Solving the proposed linear TPBVP sequence in a recursive manner leads to the optimal control law and the optimal trajectory in the form of rapid convergent series. Finally, a non-linear example and several linear examples are given to verify the reliability and efficiency of the proposed method.
引用
收藏
页码:539 / 553
页数:15
相关论文
共 50 条
[41]   CLASS OF SINGULARLY PERTURBED, NON-LINEAR, FIXED-ENDPOINT CONTROL PROBLEMS [J].
CHOW, JH .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1979, 29 (02) :231-251
[42]   Application of the homotopy perturbation method to linear and nonlinear Schrodinger equations [J].
Mousa, Mohamed M. ;
Ragab, Shahwar F. .
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2008, 63 (3-4) :140-144
[43]   SEQUENTIAL CONVEX PROGRAMMING FOR NON-LINEAR STOCHASTIC OPTIMAL CONTROL [J].
Bonalli, Riccardo ;
Lew, Thomas ;
Pavone, Marco .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2022, 28
[44]   Application of Optimal Homotopy Asymptotic Method for Solving Linear Delay Differential Equations [J].
Anakira, N. Ratib ;
Alomari, A. K. ;
Hashim, I. .
2013 UKM FST POSTGRADUATE COLLOQUIUM, 2013, 1571 :1013-1019
[45]   An iterative GL(n, R) method for solving non-linear inverse vibration problems [J].
Liu, Chein-Shan .
NONLINEAR DYNAMICS, 2013, 74 (03) :685-699
[46]   Identification of diffusion parameters in a non-linear convection-diffusion equation using adaptive homotopy perturbation method [J].
Liu, Tao ;
Liu, Songshu .
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2018, 26 (04) :464-478
[47]   Feedback controller design for linear and a class of nonlinear optimal control problems [J].
Shirazian, Mohammad ;
Effati, Sohrab .
OPTIMAL CONTROL APPLICATIONS & METHODS, 2014, 35 (03) :271-285
[48]   A new analytical method for solving a class of nonlinear optimal control problems [J].
Matinfar, M. ;
Saeidy, M. .
OPTIMAL CONTROL APPLICATIONS & METHODS, 2014, 35 (03) :286-302
[49]   Hornotopy perturbation method for linear programming problems [J].
Najafi, H. Saberi ;
Edalatpanah, S. A. .
APPLIED MATHEMATICAL MODELLING, 2014, 38 (5-6) :1607-1611
[50]   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