title: Intermittent control of coexisting attractors.
abstract: This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This intermittent control uses an impulsive force to perturb one of the system attractors in order to switch the system response onto another attractor. This is carried out by bringing the perturbed state into the desired basin of attraction. The method has been applied to control both smooth and non-smooth systems, with the Duffing and impact oscillators used as examples. The strength of the intermittent control force is also considered, and a constrained intermittent control law is introduced to investigate the effect of limited control force on the efficiency of the controller. It is shown that increasing the duration of the control action and/or the number of control actuations allows one to successfully switch between the stable attractors using a lower control force. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.
authors.affiliation: Centre for Applied Dynamics Research, School of Engineering, King's College, University of Aberdeen, Aberdeen, UK.
authors.forename: Yang
authors.initials: Y
authors.lastname: Liu
authors.forename: Marian
authors.initials: M
authors.lastname: Wiercigroch
authors.forename: James
authors.initials: J
authors.lastname: Ing
authors.forename: Ekaterina
authors.initials: E
authors.lastname: Pavlovskaia
keywords: Duffing oscillator; coexisting attractors; impact oscillator; intermittent control; non-autonomous dynamical systems