Summary
This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.
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Communicated by Stephen Wiggins
This work has been supported by CNPq (Brazil) under Grant 200597/90-6 and SERC (UK) under Grant GR/H 35286.
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Aguirre, L.A., Billings, S.A. Closed-loop suppression of chaos in nonlinear driven oscillators. J Nonlinear Sci 5, 189–206 (1995). https://doi.org/10.1007/BF01212954
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DOI: https://doi.org/10.1007/BF01212954