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Adaptive neural control for MIMO nonlinear systems with state time-varying delay

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Abstract

In this paper, adaptive neural control is proposed for a class of multi-input multi-output (MIMO) nonlinear unknown state time-varying delay systems in block-triangular control structure. Radial basis function (RBF) neural networks (NNs) are utilized to estimate the unknown continuous functions. The unknown time-varying delays are compensated for using integral-type Lyapunov-Krasovskii functionals in the design. The main advantage of our result not only efficiently avoids the controller singularity, but also relaxes the restriction on unknown virtual control coefficients. Boundedness of all the signals in the closed-loop of MIMO nonlinear systems is achieved, while The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The feasibility is investigated by two simulation examples.

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Author information

Authors and Affiliations

  1. Computer and Information Engineering College, Guangxi Teachers Education University, Nanning Guangxi, 530023, China

    Ruliang Wang

  2. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning Guangxi, 530023, China

    Kunbo Mei & Yanbo Li

  3. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan Hubei, 430074, China

    Chaoyang Chen

  4. Information Engineering College, Capital Normal University, Beijing, 100048, China

    Hebo Mei

  5. School of Education Sciences, Guangxi Teachers Education University, Nanning Guangxi, 530023, China

    Zhifang Yu

Authors
  1. Ruliang Wang
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  3. Chaoyang Chen
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  4. Yanbo Li
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Corresponding author

Correspondence to Ruliang Wang.

Additional information

This work was partly supported by the National Natural Science Foundation of China (Nos. 60864001, 61074124).

Ruliang WANG received his B.A. degree in Mathematics from Guangxi Normal University, China, M.A. degree in Mathematics from Guangxi Normal University, China, and Ph.D. degree in Automation Science and Engineering from South China University of Technology, China, in 1984, 1991 and 2001, respectively. Currently, he is a professor with Computer and Information Engineering College, Guangxi Teachers Education University, Nanning, China. His research interests include nonlinear control systems, adaptive control, and fuzzy control theory.

Kunbo MEI was born in Nanchang, China. Currently, He is working towards the M.S. degree at School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, China. His research interests include adaptive control, nonlinear time-delay systems, and fuzzy control systems.

Chaoyang CHEN was born in Xiangtan, China, 1984. He received his M.A. degree from Guangxi Teachers Education University, Guangxi, China, 2010. Currently, he is working towards the Ph.D. degree at the Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, China. His research interests include adaptive control, nonlinear time-delay systems, and networked control systems.

Yanbo LI received her B.A. degree in Mathematics from Lu Dong University, China, M.A. degree in Mathematics from Guangxi University, China, and Ph.D. degree in Control Engineering and Theory from Ocean University of China, China, in 2001, 2004 and 2007, respectively. Currently, she is an associate professor in Guangxi Teachers Education University, Nanning, China. Her research interests include nonlinear control systems and variable structure control theory.

Hebo MEI was born in Poyang, China, in 1987. He is working towards the M.S. degree at Information Engineering College, Capital Normal University, Beijing, China. His research interests include adaptive control, nonlinear time-delay systems.

Zhifang YU was born in Shangrao, China. Currently, He is working towards the M.S. degree at School of Education Sciences, Guangxi Teachers Education University, Nanning, China. His research interests include adaptive control and fuzzy control systems.

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Wang, R., Mei, K., Chen, C. et al. Adaptive neural control for MIMO nonlinear systems with state time-varying delay. J. Control Theory Appl. 10, 309–318 (2012). https://doi.org/10.1007/s11768-012-0281-x

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  • DOI: https://doi.org/10.1007/s11768-012-0281-x

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