Abstract
In this paper, a robust stability analysis method for feedback linearization using neural networks is presented. The robust regulation problem of nonlinear system with external disturbance is considered. The feedforward neural networks with one hidden layer are used to approximate the uncertain nonlinear system. The approximation errors are treated as the structured uncertainties with the known bounds. For these external disturbance and structured uncertainties, stability robustness of the closed system is analyzed in both input-output sense and Lyapunov sense.
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
Slotine, J.E., Li, W.: Applied nonlinear control. Prentice-Hall, Englewood Cliffs (1991)
Isidori, A.: Nonlinear control systems. Springer, Berlin (1989)
Sastry, S., Bodson, M.: Adaptive Control: Stability, Convergence, and Robustness. Prentice-Hall, Englewood Cliffs (1989)
Marino, R., Tomei, P.: Nonlinear Control Design. Prentice-Hall, Englewood Cliffs (1995)
Narendra, K.S., Paethasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Networks 1(1), 1–27 (1990)
Narendra, K.S., Paethasarathy, K.: Gradient methods for the optimization of dynamical systems containing neural networks. IEEE Trans. Neural Networks 2(2), 252–262 (1991)
Chen, F.C., Khalil, H.K.: Adaptive control of a class of nonlinear discrete-time systems using neural networks. IEEE Trans. Automat. Contr. 40(5), 791–801 (1995)
Teixeira, E.P., Faria, E.B., Breunig, A.: The use of feedforward neural networks to cancel nonlinearities of dynamic systems. In: Proc. ICNN 1997, Houston, vol. 2, pp. 767–772 (1997)
Chen, S., Billings, S.A.: Neural networks for nonlinear dynamic system modelling and identification. International journal of control 56(2), 319–346 (1992)
Suykens, J.A.K., Vandewalle, J.P.L., De Moor, B.D.R.: Artificial neural networks for modelling and control of non-linear systems. Kluwer Academic Publishers, Boston (1995)
Safonov, M., Athans, M.: A multiloop generalization of the circle criterion for stability margin analysis. IEEE Trans. Automat. Contr. 26(2), 415–421 (1981)
Rosenbrock, H.H.: Multivariable circle criterion in recent Mathematical Development in Control, Bell, D.J. (ed.) Academic, New York (1973)
Cook, P.A.: Modified multivariable circle theorems in recent Mathematical Development in Control, Bell, D.J. (ed.) Academic, New York (1973)
Parisini, T., Zoppoli, R.: Neural networks for feedback feedforward nonlinear control systems. IEEE Trans. Neural Networks 5(3), 436–449 (1994)
Schiffmann, W.H., Geffers, H.W.: Adaptive control of dynamic systems by back propagation networks. Neural Networks 6, 517–524 (1993)
Meyer-Base, A.: Perturbation analysis of a class of neural networks. In: Proc. ICNN 1997, Houston, vol. 2, pp. 825–828 (1997)
Werbos, P.: Back propagation through time: What it does and how to do it. Proc. of the IEEE 78(10), 1150–1560 (1990)
Miller, W.T., Sutton, R.S., Werbos, P.J.: Neural networks for control. MIT Press, Cambridge (1990)
Vidyasagar, M.: Nonlinear system analysis. Prentice-Hall, Englewood Cliffs (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lee, JB., Park, CW., Sung, HG. (2006). Robust Stability of Nonlinear Neural-Network Modeled Systems. In: Jiao, L., Wang, L., Gao, Xb., Liu, J., Wu, F. (eds) Advances in Natural Computation. ICNC 2006. Lecture Notes in Computer Science, vol 4221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881070_59
Download citation
DOI: https://doi.org/10.1007/11881070_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45901-9
Online ISBN: 978-3-540-45902-6
eBook Packages: Computer ScienceComputer Science (R0)