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H ∞ Control Design Using Dynamic Neural Networks

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Abstract

In this paper, a new approach is investigated for adaptive dynamic neural network-based H ∞ control, which is designed for a class of non-linear systems with unknown uncertainties. Currently, non-linear systems with unknown uncertainties are commonly used to efficiently and accurately express the real practical control process. Therefore, it is of critical importance but a great challenge and still at its early age to design a stable and robust controller for such a process. In the proposed research, dynamic neural networks were constructed to precisely approximate the non-linear system with unknown uncertainties first, a non-linear state feedback H ∞ control law was designed next, then an adaptive weighting adjustment mechanism for dynamic neural networks was developed to achieve H ∞ regulation performance, and last a recurrent neural network was employed as a neuro-solver to efficiently and numerically solve the standard LMI problem so as to obtain the appropriate control gains. Finally, case studies further verify the feasibility and efficiency of the proposed research.

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Abbreviations

LMI:

Liner matrix inequality

LDI:

Linear differential inclusion

References

  1. Gupta MM, Rao DH (eds) (1994). Neuro control systems. IEEE Press, New York

    Google Scholar 

  2. Suykens JAK, Vanderwalle B and De Moor B (1996). Artificial neural networks for modelling and control of non-linear systems. Kluwer, Norwell

    Google Scholar 

  3. Shen Y, Hui Y and Jian G (2006). Reliable robust controller design for non-linear state-delayed systems based on neural networks. Lecture Notes Comput Sci 4234: 674–683

    Article  Google Scholar 

  4. Suykens JAK, Vandewalle J and De Moor B (1999). Lur’s systems with multilayer perceptron and recurrent neural networks: Absolute stability and dissipativity. IEEE Trans Automat Contr 44: 770–774

    Article  MATH  MathSciNet  Google Scholar 

  5. Lin C-L and Lin T-Y (2001). An design approach for neural net-based control schemes. IEEE Trans Automat Contr 46(10): 1599–1605

    Article  MATH  Google Scholar 

  6. Mukaidanif H, Ishii Y, Tanaka Y, Bu N, Tsuji T (2004) LMI based neurocontroller for guaranteed cost control of discrete-time uncertain system. IEEE Conference on Decision and Control, Atlantis, pp 800–814

  7. Hu S and Liu Y (2004). Robust H ∞ control of multiple time-delay uncertain non-linear system using fuzzy model and adaptive neural network. Fuzzy Sets Syst 146: 403–420

    Article  MATH  MathSciNet  Google Scholar 

  8. Lin C-L and Lin T-Y (2002). Approach to adaptive neural net-based H ∞ control design. IEEE Proc Control Theory Appl 149(4): 331–342

    Article  Google Scholar 

  9. Lin C-L, Lai C-C and Huang T-H (2000). A neural networks for linear matrix inequality problems. IEEE Trans Neural Networks 11(5): 1078–1092

    Article  Google Scholar 

  10. Rovithakis GA and Christodoulou MA (1995). Direct adaptive regulation of unknown non-linear dynamical systems via dynamic neural networks. IEEE Trans Syst Man Cybernet 25(12): 1578–1594

    Article  Google Scholar 

  11. Rovithakis GA and Christodoulou MA (1997). Neural adaptive regulation of unknown non-linear dynamical systems. IEEE Trans Syst Man Cybernet B 27(5): 810–822

    Article  Google Scholar 

  12. Rovithakis GA (1999). Tracking control of multi-input affine non-linear dynamical systems with unknown nonlinearities using dynamical neural networks. IEEE Trans Syst Man Cybernet B 29(2): 179–189

    Article  Google Scholar 

  13. Rovithakis GA (1999). Robust neural adaptive stabilization of unknown systems with measurement noise. IEEE Trans Syst Man Cybernet B 29(3): 453–459

    Article  MathSciNet  Google Scholar 

  14. Kosmatopoulos E, Polycarpou M, Christodoulou M and Ioannou P (1995). Higher-order neural networks structures for identification of dynamical systems. IEEE Trans Neural Networks 6(2): 422–431

    Article  Google Scholar 

  15. Dempo A, Farotimi O and Kailath T (1991). Higher-order absolutely stable neural networks. IEEE Trans Circ Syst 38: 57–65

    Article  Google Scholar 

  16. Stoorvogel A (1992) The H ∞ control problem: a state space approach. Upper Saddle River, NJ: Prentice-Hall

  17. Boyd S, Ghaoui LE, Feron E and Balakrishnan V (1994). Linear matrix inequality in system and control theory. SIAM, Philadelphia

    Google Scholar 

  18. Steward GW (1973). Introduction to matrix computation. Academic Press, Orlando

    Google Scholar 

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Authors and Affiliations

  1. Institute of Nonlinear Complex Systems, China Three Gorges University, Yichang, Hubei, 443002, China

    Yanjun Shen

  2. Department of Electrical and Computer Engineering, Dalhousie University, Halifax, Canada

    Weimin Shen

Authors
  1. Yanjun Shen
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  2. Weimin Shen
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Correspondence to Yanjun Shen.

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Shen, Y., Shen, W. H ∞ Control Design Using Dynamic Neural Networks. Neural Process Lett 27, 97–113 (2008). https://doi.org/10.1007/s11063-007-9062-9

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  • DOI: https://doi.org/10.1007/s11063-007-9062-9

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