Synchronization of Duffing-Holmes oscillators using stable neural network controller

Authors:
Suwat Kuntanapreeda
Affiliations:
Department of Mechanical and Aerospace Engineering, Faculty of Engineering, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
Venue:
ICCCI'10 Proceedings of the Second international conference on Computational collective intelligence: technologies and applications - Volume Part III
Year:
2010

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Abstract

This paper presents a neural network controller for synchronization of two Duffing-Holmes oscillators. A Duffing-Holmes oscillator is a chaotic system describing a dynamics of the forced vibration of a buckled elastic beam. The controller is a feedforward neural network trained to drive the first Duffing-Holmes oscillator so that its states converge to those of the other Duffing-Holmes. The training scheme is based on a model reference strategy with imposing stability conditions on the controller's parameters. The stability condition guarantees the convergence of the synchronization errors. Numerical simulations are conducted to illustrate the feasibility and effectiveness of the stable neural network controller.