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Direct adaptive neural control for stabilization of nonlinear time-delay systems

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Abstract

This paper is concerned with the problem of adaptive neural control for uncertain nonlinear strict-feedback time-delay systems with unknown virtual control coefficients. Radial basis function (RBF) neural networks are employed to directly approximate unknown virtual control signals, and then the adaptive neural control law is constructed by Lyapunov-Krasovskii functionals and backstepping. In order to avoid encountering a large number of adaptive parameters when using RBF neural networks as function approximators, an unknown constant, instead of unknown neural weights themselves, is employed as the estimated parameter. This technique makes only one adaptive parameter tuned online, thus significantly alleviating the burdensome computation. Meanwhile, some continuous functions are introduced to overcome the design difficulty originating from the use of one adaptive parameter. The proposed adaptive control guarantees the boundedness of all the signals in the closed-loop system. Simulation studies are presented to illustrate the effectiveness of the scheme.

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Authors and Affiliations

  1. College of Automation, South China University of Technology, Guangzhou, 510641, China

    Min Wang

  2. Institute of Complexity Science, Qingdao University, Qingdao, 266071, China

    Min Wang, SiYing Zhang, Bing Chen & Fei Luo

Authors
  1. Min Wang
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  2. SiYing Zhang
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  3. Bing Chen
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  4. Fei Luo
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Correspondence to Min Wang.

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Wang, M., Zhang, S., Chen, B. et al. Direct adaptive neural control for stabilization of nonlinear time-delay systems. Sci. China Inf. Sci. 53, 800–812 (2010). https://doi.org/10.1007/s11432-010-0075-z

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  • DOI: https://doi.org/10.1007/s11432-010-0075-z

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