caa a22 4500 445360305 CHVBK 20180317142913.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s11071-010-9860-x doi (NATIONALLICENCE)springer-10.1007/s11071-010-9860-x A robust method on estimation of Lyapunov exponents fromanoisy time series [Elektronische Daten] [Caixia Yang, Christine Wu] Lyapunov exponents can indicate the asymptotic behaviors of nonlinear systems, and thus can be used for stability analysis. However, it is notoriously difficult to estimate these exponents reliably from experimental data due to the measurement error (noise). In this paper, a novel method for estimating Lyapunov exponents from a time series in the presence of additive noise corruption is presented. The method combines the ideas of averaging the noisy data to form new neighbors and of nonlinear mapping to determine neighborhood mapping matrices. Two case studies of balancing control of a bipedal robot and the Lorenz systems are presented to demonstrate the efficacy of the proposed method. The bipedal robot system has two negative Lyapunov exponents while the Lorenz system has one positive, zero, and negative exponents, respectively. It is shown that, as compared with the existing methods, our proposed one is more robust to the ratio of signal to noise, and is particularly effective in estimating negative Lyapunov exponents. We believe that the work can contribute significantly to the stability analysis of nonlinear systems using a noisy time series. Springer Science+Business Media B.V., 2010 Stability analysis nationallicence Lyapunov exponents nationallicence Noisy time series nationallicence Nonlinear mapping nationallicence Yang Caixia Department of Mechanical and Manufacturing Engineering, University of Manitoba, R3T 5V6, Winnipeg, MB, Canada aut Wu Christine Department of Mechanical and Manufacturing Engineering, University of Manitoba, R3T 5V6, Winnipeg, MB, Canada aut Nonlinear Dynamics Springer Netherlands 64/3(2011-05-01), 279-292 0924-090X 64:3<279 2011 64 11071 https://doi.org/10.1007/s11071-010-9860-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9860-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yang Caixia Department of Mechanical and Manufacturing Engineering, University of Manitoba, R3T 5V6, Winnipeg, MB, Canada aut NATIONALLICENCE 700 1- Wu Christine Department of Mechanical and Manufacturing Engineering, University of Manitoba, R3T 5V6, Winnipeg, MB, Canada aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 64/3(2011-05-01), 279-292 0924-090X 64:3<279 2011 64 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer