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Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

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Abstract

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems composed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.

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References

  1. Tanaka K, Wang H O. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001

    Google Scholar 

  2. Zhou W N, Meng P Y. LMI-based H∞ control design with regional stability constraint for T-S fuzzy system. Proc 2005 Intern Conf Mach Learn Cybern. 2005, 2: 868–873

    Article  Google Scholar 

  3. Ma J, Feng G. An approach to H∞ control of fuzzy dynamic systems. Fuzzy Sets Syst, 2003, 137(3): 367–386

    Article  MATH  Google Scholar 

  4. Suykens J A K, Vandewalle J P L, De Moor B L R. Artificial Neural Networks for Modeling and Control of Non-Linear Systems. Norwell, MA: Kluwer Academic Publishers, 1996

    Google Scholar 

  5. NØrgaard M, Ravn O, Poulsen N K, et al. Neural Networks for Modeling and Control of Dynamic Systems. London, Berlin, Heidelberg: Springer-Verlag, 2000

    Google Scholar 

  6. Lin C M, Hsu C F. Recurrent-neural-network-based adaptive-backstepping control for induction servomotors. IEEE Trans Industr Electr, 2005, 52(6): 1677–1684

    Article  Google Scholar 

  7. Er M J, Gao Y. Robust adaptive control of robot manipulators using generalized fuzzy neural networks. IEEE Trans Industr Electr, 2003, 50(3): 620–628

    Article  Google Scholar 

  8. Lin C M, Hsu C F. Supervisory recurrent fuzzy neural network control of wing rock for slender delta wings. IEEE Trans Fuzzy Syst, 2004, 12(5): 733–742

    Article  Google Scholar 

  9. Tanaka K, Sugeno M. Stability and design of fuzzy control systems. Fuzzy Sets Syst, 1992, 45(2): 135–156

    Article  MATH  Google Scholar 

  10. Tanaka K. An approach to stability criteria of neural-network control system. IEEE Trans Neural Networks, 1996, 7(3): 629–642

    Article  Google Scholar 

  11. Tanaka K. Stability and stabilizability of fuzzy-neural-linear control systems. IEEE Trans Fuzzy Syst, 1995, 3(4): 438–447

    Article  Google Scholar 

  12. Liao X F, Chen G R, Sanchez E N. LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans CAS-I, 2002, 49(7): 1033–1039

    Article  Google Scholar 

  13. Limanond S, Si J. Neural-network-based control design: an LMI approach. IEEE Trans Neural Networks, 1998, 9(6): 1422–1429

    Article  Google Scholar 

  14. Boyd S P, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994

    MATH  Google Scholar 

  15. Wu H N, Cai K Y. H2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities. Fuzzy Sets Syst, 2004, 148(3): 411–429

    Article  MATH  Google Scholar 

  16. Lin C L, Lin T Y. An H∞ design approach for neural net-based control schemes. IEEE Trans Automatic Control, 2001, 46(10): 1599–1605

    Article  MATH  Google Scholar 

  17. Liao X F, Chen G R, Sanchez E N. Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural Networks, 2002, 15(7): 855–866

    Article  Google Scholar 

  18. Adachi M, Aihara K. Associative dynamics in a chaotic neural network. Neural Networks, 1997, 10(1): 83–98

    Article  Google Scholar 

  19. He G G, Cao Z T, Zhu P, et al. Controlling chaos in a chaotic neural network. Neural Networks, 2002, 16(8): 1195–1200

    Article  Google Scholar 

  20. Cheng C J, Liao T L, Hwang C C. Exponential synchronization of a class of chaotic neural networks. Chaos, Solitons and Fractals, 2005, 24(1): 197–206

    Article  MATH  Google Scholar 

  21. Tian Y P. Delayed feedback control of chaos in a switched arrival system. In: Proceedings of 2005 International Conference on Physics and Control, 2005. 355–359

  22. Kobori H, Ikoda K, Nakayama K. A model of dynamic associative memory. IEEE Internat Confer Neural Networks, 1996, 2: 804–809

    Google Scholar 

  23. Gahinet P, Nemirovski A, Laub A J, et al. LMI Control Toolbox-For Use with Matlab. Natick, MA: The MATH Works, Inc., 1995

    Google Scholar 

  24. Chandrasekharan P C. Robust Control of Linear Dynamical Systems. London: Academic Press, 1996

    Google Scholar 

  25. Moore J B, Anderson B D O. A generalization of the Popov criterion. J Franklin Institute, 1968, 285(6): 488–492

    Article  MATH  Google Scholar 

  26. Rios-Patron E. A general framework for the control of nonlinear systems. PHD thesis, University of Illinois, 2000

  27. Liu M Q. Discrete-time delayed standard neural network model and its application. Sci China Ser F-Inf Sci, 2006, 49(2): 137–154

    Article  MATH  Google Scholar 

  28. Xie L, de Souza C E. Robust H∞ control for linear systems with norm-bounded time-varying uncertainty. IEEE Trans Automatic Control, 1992, 37(8): 1188–1191

    Article  Google Scholar 

  29. Xu S Y, Lam J. Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers. IEEE Trans Fuzzy Syst, 2005, 13(1): 82–93

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China

    Liu MeiQin

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  1. Liu MeiQin
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Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60504024), the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y106010), and the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP), China (Grant No. 20060335022)

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Liu, M. Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback. SCI CHINA SER F 50, 636–656 (2007). https://doi.org/10.1007/s11432-007-0043-4

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  • DOI: https://doi.org/10.1007/s11432-007-0043-4

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