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Part of the book series: Studies in Computational Intelligence ((SCI,volume 112))

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This chapter presents the design of an adaptive recurrent neural observer for nonlinear systems, whose mathematical model is assumed to be unknown. The observer is based on a recurrent high order neural network (RHONN), which estimates the state vector of the unknown plant dynamics and it has a Luenberger structure. The learning algorithm for the RHONN is implemented using an extended Kaiman filter (EKF). The respective stability analysis, on the basis of the Lyapunov approach, is included for the observer trained with an EKF and simulation results are included to illustrate the applicability of the proposed scheme.

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References

  1. R. Grover and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering, 2nd ed., Wiley, New York, USA, 1992

    MATH  Google Scholar 

  2. F. Khorrami, P. Krishnamurthy, and H. Melkote, Modeling and Adaptive Nonlinear Control of Electric Motors, Springer, Berlin Hiedelberg New York, 2003

    Google Scholar 

  3. Y. H. Kim and F. L. Lewis, High-Level Feedback Control with Neural Networks, World Scientific, Singapore, 1998

    MATH  Google Scholar 

  4. A. J. Krener and A. Isidori, Linearization by output injection and nonlinear observers, System and Control Letters, 3, 47–52, 1983

    Article  MATH  MathSciNet  Google Scholar 

  5. A. U. Levin and K. S. Narendra, Control of nonlinear dynamical systems using neural networks, Part 2: observability, identification and control, IEEE Transactions on Neural Networks, 7(1), 30–42, 1996

    Article  Google Scholar 

  6. R. Marino, Observers for single output nonlinear systems, IEEE Transactions on Automatic Control, 35, 1054–1058, 1990

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Nicosia and A. Tornambe, High-gain observers in the state and parameter estimation of robots having elastic joins, System and Control Letters, 13, 331–337, 1989

    Article  MATH  MathSciNet  Google Scholar 

  8. G. A. Rovithakis and M. A. Chistodoulou,Adaptive Control with Recurrent High-Order Neural Networks, Springer, Berlin Hiedelberg New York, 2000

    Google Scholar 

  9. E. N. Sanchez, A. Y. Alanis, and G. Chen, Recurrent neural networks trained with Kalman filtering for discrete chaos reconstruction, Dynamics of Continuous, Discrete and Impulsive Systems Series B, 13, 1–18, 2006

    Google Scholar 

  10. E. N. Sanchez and L. J. Ricalde, Trajectory tracking via adaptive recurrent neural control with input saturation, Proceedings of International Joint Conference on Neural Networks’03, Portland, Oregon, USA, July 2003

    Google Scholar 

  11. B. L. Walcott and S. H. Zak, State observation of nonlinear uncertain dynamical system, IEEE Transactions on Automatic Control, 32, 166–170, 1987

    Article  MATH  MathSciNet  Google Scholar 

  12. Q. Zhu and L. Guo, Stable adaptive neurocontrol for nonlinear discrete-time systems, IEEE Transactions on Neural Networks, 15(3), 653–662, 2004

    Article  Google Scholar 

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© 2008 Springer-Verlag Berlin Heidelberg

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(2008). Discrete-Time Neural Observers. In: Discrete-Time High Order Neural Control. Studies in Computational Intelligence, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78289-6_5

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  • DOI: https://doi.org/10.1007/978-3-540-78289-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78288-9

  • Online ISBN: 978-3-540-78289-6

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