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
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