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- Title
Solving a class of linear and non-linear optimal control problems by homotopy perturbation method.
- Authors
Effati, S.; Nik, H. Saberi
- Abstract
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.
- Subjects
HOMOTOPY theory; HOMOTOPY groups; HOMOTOPY equivalences; LINEAR systems; HAMILTONIAN systems
- Publication
IMA Journal of Mathematical Control & Information, 2011, Vol 28, Issue 4, p539
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnr018