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Robust H ∞  Control for Delayed Nonlinear Systems Based on Standard Neural Network Models

  • Mei-Qin Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3972)

Abstract

A neural-network-based robust output feedback H ∞  control design is suggested for control of a class of nonlinear systems with time delays. The design approach employs a neural network, of which the activation functions satisfy the sector conditions, to approximate the delayed nonlinear system. A full-order dynamic output feedback controller is designed for the approximating neural network. The closed-loop neural control system is transformed into a novel neural network model termed standard neural network model (SNNM). Based on the robust H ∞  performance analysis of the SNNM, the parameters of output feedback controllers can be obtained by solving some lilinear matrix inequalities (LMIs). The well-designed controller ensures the asymptotic stability of the closed-loop system and guarantees an optimal H ∞  norm bound constraint on disturbance attenuation for all admissible uncertainties.

Keywords

Output Feedback Disturbance Attenuation Global Exponential Stability Output Feedback Controller Dynamic Output Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Suykens, J.A.K., Vandewalle, J.P.L., De Moor, B.L.R.: Artificial Neural Networks for Modeling and Control of Non-linear Systems. Kluwer Academic Publishers, Norwell (1996)Google Scholar
  2. 2.
    Xu, H.J., Ioannou, P.A.: Robust Adaptive Control for a Class of MIMO Nonlinear Systems with Guaranteed Error Bounds. IEEE Trans. on Automatic Control 48(5), 728–742 (2003)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Lin, C.L., Lin, T.Y.: An H∞ Design Approach for Neural Net-based Control Schemes. IEEE Trans. on Automatic Control 46(10), 1599–1605 (2001)MATHCrossRefGoogle Scholar
  4. 4.
    Lin, F.J., Lee, T.S., Lin, C.H.: Robust H∞ Controller Design with Recurrent Neural Network for Linear Synchronous Motor Drive. IEEE Trans. on Industrial Electronics 50(3), 456–470 (2003)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Baldi, P., Atiya, A.F.: How Delays Affect Neural Dynamics and Learning. IEEE Transactions on Neural Networks 5(4), 612–621 (1994)CrossRefGoogle Scholar
  6. 6.
    Shen, Y., Zhao, G.Y., Jiang, M.H., Hu, S.G.: Stochastic High-order Hopfield Neural Networks. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 740–749. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Shen, Y., Jiang, M.H., Liao, X.X.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-varying Delays and Continuously Distributed Delays. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 156–161. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Shen, Y., Zhao, G.Y., Jiang, M.H., Mao, X.R.: Stochastic Lotka-Volterra Competitive Systems with Variable Delay. In: Huang, D.-S., Zhang, X.-P., Huang, G.-B. (eds.) ICIC 2005. LNCS, vol. 3645, pp. 238–247. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Zeng, Z., Wang, J., Liao, X.: Global Exponential Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Syst.-I: Fundamental Theory and Applications 50(10), 1353–1358 (2003)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Liu, M., Yan, G., Wang, S.: Neural-model Based Robust H∞ Controllers for Nonlinear Systems: an BMI Approach. In: International Conference on Systems, Man and Cybernetics, Hague, Netherlands, vol. 6, pp. 5876–5881 (2004)Google Scholar
  11. 11.
    Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)MATHGoogle Scholar
  12. 12.
    Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox- for Use with Matlab. The MATH Works, Inc., Natick (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mei-Qin Liu
    • 1
  1. 1.College of Electrical EngineeringZhejiang UniversityHangzhouChina

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