Stabilization of saddle steady states of conservative and weakly damped dissipative dynamical systems

An adaptive feedback method for tracking and stabilizing unknown and/or slowly varying saddle-type steady states of conservative and weakly damped dissipative dynamical systems is proposed. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter tech...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2010-08, Vol.82 (2 Pt 2), p.026205-026205, Article 026205
Main Authors: Tamasevicius, Arūnas, Tamaseviciūte, Elena, Mykolaitis, Gytis, Bumeliene, Skaidra, Kirvaitis, Raimundas
Format: Article
Language:English
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Summary:An adaptive feedback method for tracking and stabilizing unknown and/or slowly varying saddle-type steady states of conservative and weakly damped dissipative dynamical systems is proposed. We demonstrate that a conservative saddle point can be stabilized with neither unstable nor stable filter technique. The proposed controller involves both filters working in parallel. As a specific example, the Lagrange point L2 of the Sun-Earth system is discussed and the second-order saddle model is considered. Analog simulations have been performed using an inclusive nonlinear electrical circuit, imitating dynamics of a body along the Sun-Earth line. External chaotic perturbations have been used to check the robustness of the control technique.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.82.026205