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Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network

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Abstract

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion (FSE) are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions (such as global Lipschitz condition) is relaxed. Furthermore, by using appropriate Lyapunov-Krasovskii functionals, all signs in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded, and the output of the system is proved to converge to the desired trajectory. A simulation example is provided to illustrate the effectiveness of the control scheme.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, Xi’an, 710071, PRC

    Chun-Li Zhang & Jun-Min Li

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  1. Chun-Li Zhang
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  2. Jun-Min Li
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Correspondence to Chun-Li Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (No. 72103676) (partially supported by the Fundamental Research Funds for the Central Universities).

Chun-Li Zhang graduated from Linyi Normal University, PRC in 2007. She received the M. S. degree from Xidian University in 2010. She is currently a Ph.D. candidate at the Department of Applied Mathematics, Xidian University.

Her research interests include adaptive iterative learning control, neural network, robust control, and chaos synchronization.

Jun-Min Li graduated from Xidian University, PRC in 1987. He received the M. S. degree from Xidian University in 1990 and the Ph.D. degree from Xi’an Jiaotong University, PRC in 1997. He is currently a professor at the Department of Applied Mathematics, Xidian University.

His research interests include adaptive control, learning control, intelligent control, hybrid system control theory, and the networked control systems.

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Zhang, CL., Li, JM. Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network. Int. J. Autom. Comput. 8, 403–410 (2011). https://doi.org/10.1007/s11633-011-0597-x

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  • DOI: https://doi.org/10.1007/s11633-011-0597-x

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