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Robust Finite-Time H ∞ Control for Nonlinear Jump Systems via Neural Networks

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Abstract

This paper presents a neural network-based robust finite-time H ∞ control design approach for a class of nonlinear Markov jump systems (MJSs). The system under consideration is subject to norm bounded parameter uncertainties and external disturbance. In the proposed framework, the nonlinearities are initially approximated by multilayer feedback neural networks. Subsequently, the neural networks undergo piecewise interpolation to generate a linear differential inclusion model. Then, based on the model, a robust finite-time state-feedback controller is designed such that the nonlinear MJS is finite-time bounded and finite-time stabilizable. The H ∞ control is specified to ensure the elimination of the approximation errors and external disturbances with a desired level. The controller gains can be derived by solving a set of linear matrix inequalities. Finally, simulation results are given to illustrate the effectiveness of the developed theoretic results.

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Authors and Affiliations

  1. Institute of Automation, Jiangnan University, Wuxi, 214122, China

    Xiaoli Luan & Fei Liu

  2. Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd, CF37 1DL, UK

    Peng Shi

  3. School of Engineering and Science, Victoria University Melbourne, Melbourne, VIC, 8001, Australia

    Peng Shi

Authors
  1. Xiaoli Luan
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  2. Fei Liu
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  3. Peng Shi
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Corresponding author

Correspondence to Fei Liu.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Grant No. 60974001), the Program for New Century Excellent Talents in University (Grant No. 050485), Six Projects Sponsoring Talent Summits of Jiangsu, and the Engineering and Physical Sciences Research Council, UK (EP/F029195).

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Luan, X., Liu, F. & Shi, P. Robust Finite-Time H ∞ Control for Nonlinear Jump Systems via Neural Networks. Circuits Syst Signal Process 29, 481–498 (2010). https://doi.org/10.1007/s00034-010-9158-8

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  • DOI: https://doi.org/10.1007/s00034-010-9158-8

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