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arXiv · 2112.09449

Controlling coexisting attractors of a class of non-autonomous dynamical systems

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

This paper studies a control method for switching stable coexisting attractors of a class of non-autonomous dynamical systems. The central idea is to introduce a continuous path for the system's trajectory to transition from its original undesired stable attractor to a desired one by varying one of the system parameters according to the information of the desired attractor. The behaviour of the control is studied numerically for both non-smooth and smooth dynamical systems, using a sof-impact and a Duffing oscillator as examples. Special attention is given to identify the regions where the proposed control strategy is applicable by using the path-following methods implemented via the continuation platform COCO. It is shown that the proposed control concept can be implemented through either using an external control input or varying a system parameter. Finally, extensive numerical results are presented to validate the proposed control methods.

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Zhi Zhang, Joseph Páez Chávez, Jan Sieber, Yang Liu. 2021-12-17. Controlling coexisting attractors of a class of non-autonomous dynamical systems. https://doi.org/10.1016/j.physd.2021.133134

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