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Non-fragile robust finite-time H ∞ control for nonlinear stochastic itô systems using neural network

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Abstract

This paper deals with the problem of non-fragile robust finite-time H ∞ control for a class of uncertain nonlinear stochastic Itô systems via neural network. First, applying multi-layer feedback neural networks, the nonlinearity is approximated by linear differential inclusion (LDI) under statespace representation. Then, a sufficient condition is proposed for the existence of non-fragile state feedback finite-time H ∞ controller in terms of matrix inequalities. Furthermore, the problem of nonfragile robust finite-time H ∞ control is reduced to the optimization problem involving linear matrix inequalities (LMIs), and the detailed solving algorithm is given for the restricted LMIs. Finally, an example is given to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Tianjin University, Tianjin, China

    Zhiguo Yan, Guoshan Zhang & Jiankui Wang

  2. School of Electrical Engineering and Automation, Shandong Polytechnic University, Jinan, China

    Zhiguo Yan

Authors
  1. Zhiguo Yan
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  2. Guoshan Zhang
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  3. Jiankui Wang
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Correspondence to Guoshan Zhang.

Additional information

Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Jae Weon Choi.

This work was supported by the National Natural Science Foundation of China with a grant No.60674019, 61074088, and is partially supported by the Starting Research Foundation of Shandong Polytechnic University under Grant 12045501.

Zhiguo Yan received his B.E. degree in Electrical Engineering and Automation from Northeast Normal University in 2005 and an M.E. degree in Control theory and Control Engineering from Shandong Polytechnic University in 2008 and a Ph.D. degree in Control theory and Control Engineering from Tianjin University in 2011. He is currently a lecturer at the School of Electrical Engineering and Automation in Shandong Polytechnic University. His research interests include linear and nonlinear stochastic control, descriptor systems, robust control.

Guoshan Zhang received his Bachelor’s degree in Mathematics from Northeast Normal University, China, in 1983. He received his master degree in Mathematics and a Ph.D. degree in Industrial Automation from Northeastern University, China, in 1989 and 1996, respectively. He joined School of Electrical Engineering and Automation, Tianjin University in 2003, and is currently a professor. He was a visiting scholar with Curtin University of Technology, Australia, from September to November in 2009. His research interests cover descriptor systems, nonlinear systems, robust control and optimal control.

Jiankui Wang received his Bachelor’s degree from Shandong Normal University, Jinan, China, in 2000, an M.S. degree in applied mathematics from Huazhong University of Science and Technology, Wuhan, China, in 2003, and a Ph.D. degree in control theory from the Chinese Academy of Sciences, Beijing, China, in 2006. From 2007 to 2008 he was a Postdoctoral Fellow in National University of Singapore, Singapore. Since 2008, he has been with Tianjin University, Tianjin, China. His research interests include nonlinear systems analysis and synthesis, modeling and control for autonomous underwater vehicles.

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Yan, Z., Zhang, G. & Wang, J. Non-fragile robust finite-time H ∞ control for nonlinear stochastic itô systems using neural network. Int. J. Control Autom. Syst. 10, 873–882 (2012). https://doi.org/10.1007/s12555-012-0502-6

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  • DOI: https://doi.org/10.1007/s12555-012-0502-6

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