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Optimal Control for a Class of Chaotic Systems

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  • Jianxiong Zhang
  • Wansheng Tang

Abstract

This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs). In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP). Finally, numerical examples are given to illustrate the results.

Suggested Citation

  • Jianxiong Zhang & Wansheng Tang, 2012. "Optimal Control for a Class of Chaotic Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:859542
    DOI: 10.1155/2012/859542
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    References listed on IDEAS

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    1. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
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    5. Sun, Huijing & Cao, Hongjun, 2008. "Chaos control and synchronization of a modified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1442-1455.
    6. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    7. Zhang, Jianxiong & Tang, Wansheng, 2009. "Analysis and control for a new chaotic system via piecewise linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2181-2190.
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    Cited by:

    1. Carmen Nejneru & Anca Nicuţă & Boris Constantin & Liliana Rozemarie Manea & Mirela Teodorescu & Maricel Agop, 2013. "Dynamics Control of the Complex Systems via Nondifferentiability," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Shukai Li & Jianxiong Zhang & Wansheng Tang, 2013. "Stabilization Strategies of Supply Networks with Stochastic Switched Topology," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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