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Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays

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  • Control Theory
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Abstract

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.

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Authors and Affiliations

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

    Weisheng Chen & Li Zhang

Authors
  1. Weisheng Chen
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  2. Li Zhang
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Correspondence to Weisheng Chen.

Additional information

Recommended by Editorial Board member Eun Tai Kim under the direction of Editor Young Il Lee. This work was supported by National Natural Science Foundation of China under grand 60804021, and partly supported by National Natural Science Foundation of China under grand 60974139, 60702063.

Weisheng Chen received his B.S. degree in the Department of Mathematics from Qufu Normal University, Qufu, China, in 2000, and his M.S. and Ph.D. degrees in the Department of Applied Mathematics from Xidian University, Xi’an, China, in 2004 and 2007, respectively. From 2008 to 2009, he is a Visiting Scholar in the Automation School at Southeast University, Nanjing, China. From 2009, he is a post doctoral candidate in the School of Electronic Engineering, Xidian University, Xi’an, China, and is currently an Associate Professor in the Department of Applied Mathematics, Xidian University, China. He has authored or coauthored more than 40 journal and conference publications. His research interests include neural network control, backstepping control, adaptive control, learning control for uncertain nonlinear systems such as time-delay or stochastic nonlinear systems and so on.

Li Zhang received her B.S. and M.S. degrees in the Department of Mathematics from Shaanxi Normal University, Xi’an, China, in 2000 and 2003, respectively, and her Ph.D. degree in the Department of Applied Mathematics from Xidian University, Xi’an, China, in 2008. Currently she is an Associate Professor in the Department of Applied Mathematics, Xidian University, China. Her research interests include nonlinear dynamic systems, partial differential equations and so on.

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Chen, W., Zhang, L. Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays. Int. J. Control Autom. Syst. 8, 177–186 (2010). https://doi.org/10.1007/s12555-010-0201-0

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