English

Optimal Control of Nonlinear Systems Using the Homotopy Perturbation Method

Optimization and Control 2014-09-18 v1

Abstract

This paper presents a new method for solving a class of nonlinear optimal control problems with a quadratic performance index. In this method, first the original optimal control problem is transformed into a nonlinear two-point boundary value problem (TPBVP) via the Pontryagin's maximum principle. Then, using the Homotopy Perturbation Method (HPM) and introducing a convex homotopy in topologic space, the nonlinear TPBVP is transformed into a sequence of linear time-invariant TPBVP's. By solving the presented linear TPBVP sequence in a recursive manner, the optimal control law and the optimal trajectory are determined in the form of infinite series. Finally, in order to obtain an accurate enough sub-optimal control law, an iterative algorithm with low computational complexity is introduced. An illustrative example demonstrates the simplicity and efficiency of proposed method.

Keywords

Cite

@article{arxiv.1409.4806,
  title  = {Optimal Control of Nonlinear Systems Using the Homotopy Perturbation Method},
  author = {Amin Jajarmi and Hamidreza Ramezanpour and Arman Sargolzaei and Pouyan Shafaei},
  journal= {arXiv preprint arXiv:1409.4806},
  year   = {2014}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1202.1679

R2 v1 2026-06-22T05:58:23.168Z