Skip to main content
Springer Nature Link
Log in

Reliable Robust Controller Design for Nonlinear State-Delayed Systems Based on Neural Networks

  • Conference paper
Neural Information Processing (ICONIP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4234))

Included in the following conference series:

Abstract

An approach is investigated for the adaptive guaranteed cost control design for a class of nonlinear state-delayed systems. The nonlinear term is approximated by a linearly parameterized neural networks(LPNN). A linear state feedback H  ∞  control law is presented. An adaptive weight adjustment mechanism for the neural networks is developed to ensure H  ∞  regulation performance. It is shown that the control gain matrices and be transformed into a standard linear matrix inequality problem and solved via a developed recurrent neural network.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Suykens, J.A.K., Vandewalle, J., De Moor, B.: Artificial neural networks for modelling and control of nonlinear systems. Kluwer Academic Publishers, Boston (1996)

    Google Scholar 

  2. Bass, E., Lee, K.Y.: Robust control of nonlinear system using norm-bounded neural networks. In: IEEE Int. Conf. on Neural Networks, vol. 4, pp. 2524–2529 (1994)

    Google Scholar 

  3. Lin, C.L.: Control of perturbed systems using neural networks. IEEE trans. Neural Netw. (9), 1046–1050 (1998)

    Article  Google Scholar 

  4. Suykens, J.A.K., Vandewalle, J., De Moor, B.: Artificial Neural Networks for Modelling and Control of nonlinear system. Kluwer, Norwell (1996)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Tanaka, K.: An approach to stability criteria of neural-network control systems. IEEE Trans. Neural Netw. (7), 629–642 (1996)

    Article  Google Scholar 

  7. Leu, Y.G., Lee, T.T., Wang, W.Y.: Online tuning of fuzzy-neural network for adaptive control of nonlinear dynamical systems. IEEE Trans. Syst. Man. Cybern. Part B (27), 1034–1043 (1997)

    Article  Google Scholar 

  8. Limanond, S., Si, J.: Neural-network-based control design: an LMI approach. IEEE Trans. Neural Netw. 9, 1429–1442 (1998)

    Article  Google Scholar 

  9. Suykens, J.A.K., Vandewalle, J., De Moor, B.: Artificial Neural Networks for Modelling and Control of Nonlinear Systems. Kluwer Academic Publishers, Norwell (1996)

    Google Scholar 

  10. Lin, C.-L., Lin, T.-Y.: An Design Approach for Neural Net-based Control Schemes. IEEE Trans. On. Automatic control (46), 1599–1605 (2001)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. Dugard, L., Verriest, E.I.: Stability and control of time-delay systems, Prentice Hall, Springer-Verlag, Berlin (1997)

    Google Scholar 

  13. Lee, J.H., Kim, S.W., Kwon, W.H.: Memoryless H  ∞  controllers for state delayed systems. IEEE Trans. Autom. Control (39), 159–162 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Niculescu, S.I.: H  ∞  memoryless control with an a-stability constraint for time-delay systems: An LMI approach. IEEE Trans. Autom. Control (43), 739–748 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. Choi, H.H., Chong, M.J.: An LMI approach to H  ∞  controller design for linear time-delays. Automatical (3), 737–739 (1997)

    Article  Google Scholar 

  16. Kosmatopoulos, E.B., Polycarpou, M.M., Christodoulou, M.A., Ioan, P.A.: High-order neural networks structures for identification of dynamical systems. IEEE Trans. Neural Networks 6, 422–431 (1995)

    Article  Google Scholar 

  17. Sanner, R.M., Slotine, J.J.E.: Structurally dynamic wavelet networks for the adaptive control of uncertain robotic systems. In: Proc. IEEE 34th Conf. Decision and Control, New Orleans, LA, pp. 2460–2467 (December 1995)

    Google Scholar 

  18. Polycarpou, M.M., Ioannou, P.A.: Identification and control of nonlinear systems using neural network models: Design and stability analysis, Dept. Eng. Sys., Southern Calif., Los Angeles, Tech. Rep. (1991)

    Google Scholar 

  19. Sanchez, E.N., Perez, J.P.: Input-to-state stability (ISS) analysis for dynamic NN. IEEE Trans. Circuits Syst. I (46), 1395–1398 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  21. Stewart, G.W.: Introduction to matrix computation. Academic Press, Orlando (1973)

    Google Scholar 

  22. Chun-Liang, L., Chi-Chih, L., Teng-Hsien, H.: A neural networks for linear matrix inequality problems. IEEE Trans. On neural networks (11), 1078–1092 (2000)

    Article  Google Scholar 

  23. Stoorvogel, A.: The H  ∞  Control Problem: A state Space Approach. Prentice-Hall, Upper Saddle River (1992)

    MATH  Google Scholar 

  24. Marcus, C.M., Westervelt, R.M.: Stability of analog neural networks with time delay. Phys. Rev. A 39, 347–359 (1989)

    MathSciNet  Google Scholar 

  25. Campbell, S.A., Driessche, P.: Frustration: stability and delay induced oscillations in a neural network model. SIAM J. Appl. Math. 56, 245–255 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  26. Baldi, P., Atiya, A.F.: How delays affect neural dynamics and learning. IEEE Trans. Neural Networks (5), 612–621 (1994)

    Article  Google Scholar 

  27. Stoorvogel, A.: The H  ∞  Control Problem: A State Space Approach. Prentice-Hall, Upper Saddle River (1992)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Nonlinear Complex system, College of Science, Three Gorges University, Yichang, Huibei, 443002, China

    Yanjun Shen, Hui Yu & Jigui Jian

Authors
  1. Yanjun Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jigui Jian
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, The Chinese Univ. of Hong Kong, Shatin, N.T., Hong Kong

    Irwin King

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, New Territories,, China

    Jun Wang

  3. The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Lai-Wan Chan

  4. Department of Computer Science and Engineering & Center for Cognitive Science, The Ohio State University, OH 43210, Columbus

    DeLiang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shen, Y., Yu, H., Jian, J. (2006). Reliable Robust Controller Design for Nonlinear State-Delayed Systems Based on Neural Networks. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893295_74

Download citation

  • DOI: https://doi.org/10.1007/11893295_74

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46484-6

  • Online ISBN: 978-3-540-46485-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics