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A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems

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  • Zhong Cao
  • Xiaorong Hou

Abstract

This paper considers controller parameterization method of control for polynomial Hamiltonian systems (PHSs), which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems are stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimize control by adjusting parameters. All these results are expected to be of use in the study of control for nonlinear systems with perturbations.

Suggested Citation

  • Zhong Cao & Xiaorong Hou, 2014. "A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, June.
    • Handle: RePEc:hin:jnlmpe:806428
    DOI: 10.1155/2014/806428
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    Cited by:

    1. Yang, Jing & Hou, Xiaorong & Li, Xiaoxue & Luo, Min, 2022. "A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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