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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Grover and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering, 2nd ed., Wiley, New York, USA, 1992
F. Khorrami, P. Krishnamurthy, and H. Melkote, Modeling and Adaptive Nonlinear Control of Electric Motors, Springer, Berlin Hiedelberg New York, 2003
Y. H. Kim and F. L. Lewis, High-Level Feedback Control with Neural Networks, World Scientific, Singapore, 1998
A. J. Krener and A. Isidori, Linearization by output injection and nonlinear observers, System and Control Letters, 3, 47–52, 1983
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
R. Marino, Observers for single output nonlinear systems, IEEE Transactions on Automatic Control, 35, 1054–1058, 1990
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
G. A. Rovithakis and M. A. Chistodoulou,Adaptive Control with Recurrent High-Order Neural Networks, Springer, Berlin Hiedelberg New York, 2000
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
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
B. L. Walcott and S. H. Zak, State observation of nonlinear uncertain dynamical system, IEEE Transactions on Automatic Control, 32, 166–170, 1987
Q. Zhu and L. Guo, Stable adaptive neurocontrol for nonlinear discrete-time systems, IEEE Transactions on Neural Networks, 15(3), 653–662, 2004
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(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
Download citation
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
eBook Packages: EngineeringEngineering (R0)