Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control Article Swipe

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Zhi Zhang , Joseph Páez Chávez , Jan Sieber , Yang Liu ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1007/s11071-021-06511-2

Grazing events may create coexisting attractors and cause complex dynamics in piecewise-smooth dynamical systems. This paper studies the control of grazing-induced multistability in a soft impacting oscillator by using the time-delayed feedback control. The control switches from one of the coexisting attractors to a desired one to suppress complex dynamics near grazing events. We use path-following (continuation) techniques for non-smooth dynamical systems to investigate robustness of the controller and the parameter dependence of the controlled system. In particular, several newly developed computational methods are used, including a numerical method for analysing non-smooth delay equations and a method for calculating the Lyapunov exponents and the grazing point estimation. Numerical simulations demonstrate that the delayed feedback controller is effective, and a proper selection of the control gain and delay time can simplify the complex dynamics of the system near grazing.

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Multistability Control theory (sociology) Piecewise Attractor Robustness (evolution) Lyapunov exponent Feedback control Dynamical systems theory Mathematics Computer science Chaotic Nonlinear system Control (management) Physics Mathematical analysis Control engineering Engineering Artificial intelligence Biochemistry Chemistry Quantum mechanics Gene

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Type: article
Language: en
Landing Page: https://doi.org/10.1007/s11071-021-06511-2
PDF: https://link.springer.com/content/pdf/10.1007/s11071-021-06511-2.pdf
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Cited By: 33
References: 52
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DOI: https://doi.org/10.1007/s11071-021-06511-2

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Title: Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control

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Language: en

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Publication year: 2021

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Publication date: 2021-05-19

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Authors: Zhi Zhang, Joseph Páez Chávez, Jan Sieber, Yang Liu

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Landing page: https://doi.org/10.1007/s11071-021-06511-2

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Concepts: Multistability, Control theory (sociology), Piecewise, Attractor, Robustness (evolution), Lyapunov exponent, Feedback control, Dynamical systems theory, Mathematics, Computer science, Chaotic, Nonlinear system, Control (management), Physics, Mathematical analysis, Control engineering, Engineering, Artificial intelligence, Biochemistry, Chemistry, Quantum mechanics, Gene

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Cited by: 33

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