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

TL;DR

This paper introduces a control strategy for switching between coexisting attractors in non-autonomous dynamical systems by smoothly varying system parameters, validated through numerical experiments on non-smooth and smooth systems.

Contribution

It proposes a novel control method that enables transition between stable attractors via parameter variation, applicable to both smooth and non-smooth systems, with validation through numerical simulations.

Findings

Control method successfully switches attractors in numerical examples.

Applicable to both smooth and non-smooth dynamical systems.

Control can be implemented via external input or parameter variation.

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.