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Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones

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Abstract

In this paper, adaptive variable structure neural control is presented for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with state time-varying delays and unknown nonlinear dead-zones. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear function outside the deadband without necessarily constructing a dead-zone inverse as an added contribution. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. In addition, a modified adaptive control algorithm is given in order to avoid the high-frequency chattering phenomenon. Simulation results demonstrate the effectiveness of the approach.

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Authors and Affiliations

  1. Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou, 225009, PRC

    Tian-Ping Zhang, Cai-Ying Zhou & Qing Zhu

Authors
  1. Tian-Ping Zhang
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  2. Cai-Ying Zhou
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  3. Qing Zhu
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Corresponding author

Correspondence to Tian-Ping Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60774017 and No. 60874045).

Tian-Ping Zhang received the B. Sc. degree in mathematics from Yangzhou Teachers College, PRC, in 1986, the M. Sc. degree in operations research and control theory from East China Normal University, PRC, in 1992, and the Ph.D. degree in automatic control theory and applications from Southeast University, PRC, in 1996. From October 2005 to October 2006, he was a visiting scientist in the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. He is currently a professor in the College of Information Engineering, Yangzhou University, PRC.

His research interests include fuzzy control, adaptive control, intelligent control, and nonlinear control.

Cai-Ying Zhou received the B. Sc. degree in mathematics from Yangzhou Teachers College, PRC, in 1985. She is currently an associate professor in the College of Information Engineering, Yangzhou University, PRC.

Her research interests include computer applications and intelligent control.

Qing Zhu received the M. Sc. degree in computer applications from Yangzhou University, PRC, in 2002, and the Ph.D. degree in control theory and control engineering from Southeast University, PRC, in 2008. He is currently a lecturer at the Department of Automation, Yangzhou University. His research interests include control of time-delay systems, neural networks control, and adaptive control.

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Zhang, TP., Zhou, CY. & Zhu, Q. Adaptive variable structure control of MIMO nonlinear systems with time-varying delays and unknown dead-zones. Int. J. Autom. Comput. 6, 124–136 (2009). https://doi.org/10.1007/s11633-009-0124-5

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  • DOI: https://doi.org/10.1007/s11633-009-0124-5

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