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Output mini-max control for polynomial systems: analysis and applications

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  • Manuel Jiménez-Lizárraga
  • Michael V. Basin
  • Victoria Celeste Rodríguez Carreón
  • Pablo Cesar Rodríguez Ramírez

Abstract

This paper presents a solution to a robust optimal regulation problem for a nonlinear polynomial system affected by parametric and matched uncertainties, which is based only on partial state information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favourable value of the unknown parameter. A high-order sliding mode state reconstructor is designed for the nonlinear plant in such a way that the previously designed control can be applied for a system with incomplete information. Additionally, the matched uncertainty is also compensated by means of the same output-based regulator. The obtained algorithm is applied to control an uncertain nonlinear inductor circuit of the third order and a mechanical pendulum of the third order, successfully verifying the effectiveness of the developed approach.

Suggested Citation

  • Manuel Jiménez-Lizárraga & Michael V. Basin & Victoria Celeste Rodríguez Carreón & Pablo Cesar Rodríguez Ramírez, 2014. "Output mini-max control for polynomial systems: analysis and applications," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(9), pages 1880-1891, September.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:9:p:1880-1891
    DOI: 10.1080/00207721.2012.757385
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    References listed on IDEAS

    as
    1. Michael V. Basin & Peng Shi & Dario Calderon-Alvarez, 2011. "Central suboptimal control design for nonlinear polynomial systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 801-808.
    2. Hongli Dong & James Lam & Huijun Gao, 2011. "Distributed ℋ filtering for repeated scalar nonlinear systems with random packet losses in sensor networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(9), pages 1507-1519.
    3. Shuhui Shi & Qingling Zhang & Zhonghu Yuan, 2011. "Exponential stability and -gain analysis for a class of faulty systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(3), pages 377-387.
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