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Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 499–508 | Cite as

Hyperchaos control of the hyperchaotic Chen system by optimal control design

  • S. Effati
  • H. Saberi Nik
  • A. Jajarmi
Original Paper

Abstract

The aim of this paper is to study the chaos, optimal control, and adaptive control of the hyperchaotic Chen system. In this paper, applying the Pontryagin’s minimum principle (PMP), the optimal control inputs for the interested model are obtained with respect to the selected measure. A piecewise-spectral homotopy analysis method (PSHAM) is used for solving the hyperchaotic Chen system and the extreme conditions obtained from the PMP. Furthermore, an adaptive control approach and a parameter estimation update law are introduced for the hyperchaotic Chen system with completely unknown parameters. The control results are established using the Krasovskii–LaSalle principle. Finally, numerical simulations are included to demonstrate the effectiveness of the proposed control strategy.

Keywords

Optimal control Hyperchaotic Chen system Lyapunov function Pontryagin’s minimum principle Piecewise-spectral homotopy analysis method 

Notes

Acknowledgement

This research was supported by a grant from Ferdowsi University of Mashhad (No. MA91288SEF).

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics, School of Mathematical SciencesFerdowsi University of MashhadMashhadIran
  2. 2.Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP)Ferdowsi University of MashhadMashhadIran
  3. 3.Department of Electrical EngineeringUniversity of BojnordBojnordIran

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