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Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example
Marco BERGAMI Federico BIZZARRI Andrea CARLEVARO Marco STORACE
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E89-A
No.10
pp.2759-2766 Publication Date: 2006/10/01 Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2759 Print ISSN: 0916-8508 Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications) Category: Oscillation, Dynamics and Chaos Keyword: piecewise linear approximation, nonlinear dynamical systems, bifurcation analysis, optimization,
Full Text: PDF(432.6KB)>>
Summary:
In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.
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