Abstract
Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of the designed network be stable. In this paper, the passivity-based approach is used to derive stability conditions for dynamic neural networks with different time-scales. Several stability properties, such as passivity, asymptotic stability, input-to-state stability and bounded input bounded output stability, are guaranteed in certain senses. Numerical examples are also given to demonstrate the effectiveness of the theoretical results.
This is a preview of subscription content, log in via an institution to check access.
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
Amari, S.: Field Theory of Self-Organizing Neural Nets. IEEE Trans. Syst., Man, Cybern. 13(1), 741–748 (1983)
Forti, M., Manetti, S., Marini, M.: Necessary and Sufficient Condition for Absolute Stability of Neural Networks. IEEE Trans. on Circuit and Systems-I 41(4), 491–494 (1994)
Grossberg, S.: Competition, Decision and Consensus. J. Math. Anal. Applicat. 66(5), 470–493 (1978)
Jagannathan, S., Lewis, F.L.: Identification of Nonlinear Dynamical Systems Using Multilayered Neural Networks. Automatica 32(12), 1707–1712 (1996)
Jin, L., Gupta, M.: Stable Dynamic Backpropagation Learning in Recurrent Neural Networks. IEEE Trans. Neural Networks 10(9), 1321–1334 (1999)
Kaszkurewics, K., Bhaya, A.: On a Class of Globally Stable Neural Circuits. IEEE Trans. on Circuit and Systems-I 41(1), 171–174 (1994)
Kosmatopoulos, E.B., Polycarpou, M.M., Christodoulou, M.A., Ioannou, P.A.: High-Order Neural Network Structures for Identification of Dynamical Systems. IEEE Trans. on Neural Networks 6(2), 442–431 (1995)
Meyer-Bäse, A., Ohl, F., Scheich, H.: Singular Perturbation Analysis of Competitive Neural Networks with Different Time-Scales. Neural Comput. 8(3), 545–563 (1996)
Lewis, F.L., Liu, K., Yesildirek, A.: Multilayer Neural-Net Robot Controller with Guaranteed Tracking Performance. IEEE Trans. on Neural Network 7(2), 388–398 (1996)
Rovithakis, G.A., Christodoulouand, M.A.: Adaptive Control of Unknown Plants Using Dynamical Neural Networks. IEEE Trans. on Syst., Man and Cybern. 24(2), 400–412 (1994)
Sontag, E.D., Wang, Y.: On Characterization of the Input-to-State Stability Property. System & Control Letters 24(3), 351–359 (1995)
Shao, Z.H.: Robust Stability of Two-Time-Scale Systems with Nonlinear Uncertainties. IEEE Transactions on Automatic Control 49(1), 135–140 (2004)
Suykens, J., Moor, B., Vandewalle, J.: Robust Local Stability of Multilayer Recurrent Neural Networks. IEEE Trans. Neural Networks 11(1), 222–229 (2000)
Yu, W., Poznyak, A.S.: Indirect Adaptive Control via Parallel Dynamic Neural Networks. IEE Proceedings - Control Theory and Applications 37(1), 25–30 (1999)
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
Sandoval, A.C., Yu, W. (2006). Passivity Analysis of Dynamic Neural Networks with Different Time-Scales. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_13
Download citation
DOI: https://doi.org/10.1007/11759966_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
eBook Packages: Computer ScienceComputer Science (R0)