NDLI: A radial-basis-function network-based method of estimating Lyapunov exponents from a scalar time series for analyzing nonlinear systems stability

Content Provider	Springer Nature Link
Author	Sun, Yuming Wu, Christine Qiong
Copyright Year	2012
Abstract	Lyapunov exponents indicate the asymptotic behaviors of nonlinear systems, the concept of which is a powerful tool of the stability analysis for nonlinear systems, especially when the dynamic models of the systems are available. For real world systems, however, such models are often unknown, and estimating the exponents reliably from experimental data is notoriously difficult. In this paper, a novel method of estimating Lyapunov exponents from a time series is presented. The method combines the ideas of reconstructing the attractor of the system under study and approximating the embedded attractor through tuning a Radial-Basis-Function (RBF) network, based on which the Jacobian matrices can be easily derived, making the model-based algorithm applicable. Three case studies are presented to demonstrate the efficacy of the proposed method. The Hénon map and the Lorenz system feature spectra including not only the positive exponent, but also the negative one, while the standing biped balance system is characterized by four negative exponents. Compared with the existing methods, the numerical accuracy of the Lyapunov exponents derived through the newly proposed method is much higher regardless of their signs even in the presence of measurement noise. We believe that the work can contribute to the stability analysis of nonlinear systems of which the dynamics are either unknown or difficult to model due to complexities.
Starting Page	1689
Ending Page	1708
Page Count	20
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	70
Issue Number	2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-08-21
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stability analysis Lyapunov exponents Noisy time series Radial Basis Function (RBF) network Mechanical Engineering Automotive Engineering Mechanics Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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