Intermittent control of coexisting attractors

Research output: Contribution to journalArticle

15 Citations (Scopus)

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.
Original languageEnglish
Article number20120428
Number of pages15
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume371
Issue number1993
Early online date20 May 2013
DOIs
Publication statusPublished - 28 Jun 2013

Fingerprint

Attractor
Force Control
Force control
Basin of Attraction
Switch
Trajectory
Nonautonomous Dynamical System
Switches
Trajectories
Constrained Control
attraction
Proximity
trajectories
Time Domain
Dynamical systems
Controller
Numerical Results
actuation
dynamical systems
Experimental Results

Keywords

  • coexisting attractors
  • intermittent control
  • non-autonomous dynamical systems
  • duffing oscillator
  • impact oscillator

Cite this

Intermittent control of coexisting attractors. / Liu, Yang; Wiercigroch, Marian; Ing, James; Pavlovskaia, Ekaterina.

In: Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 371, No. 1993, 20120428 , 28.06.2013.

Research output: Contribution to journalArticle

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