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Robust Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach

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  • Cheng-Dong Yang
  • Jianlong Qiu
  • Jun-Wei Wang

Abstract

This paper addresses the problem of robust control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed performance of disturbance attenuation. Moreover, a suboptimal controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.

Suggested Citation

  • Cheng-Dong Yang & Jianlong Qiu & Jun-Wei Wang, 2014. "Robust Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, January.
    • Handle: RePEc:hin:jnlaaa:631071
    DOI: 10.1155/2014/631071
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    Cited by:

    1. Xiaona Song & Mi Wang & Shuai Song & Jingtao Man, 2018. "Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems," Complexity, Hindawi, vol. 2018, pages 1-11, October.
    2. Song, Xiaona & Wang, Mi & Song, Shuai & Wang, Zhen, 2019. "Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 371-395.

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