A simplified optimal control method for homoclinic bifurcations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)43-61
Journal / PublicationNonlinear Dynamics
Volume42
Issue number1
Publication statusPublished - Oct 2005

Abstract

A simplified optimal control method is presented for controlling or suppressing homoclinic bifurcations of general nonlinear oscillators with one degree-of-freedom. The simplification is based on the addition of an adjustable parameter and a superharmonic excitation in the force term. By solving an optimization problem for the optimal amplitude coefficients of the harmonic and superharmonic excitations to be used as the controlled parameters, the force term as the controller can be designed. By doing so, the control gain and small optimal amplitude coefficients can be obtained at lowest cost. As the adjustable parameter decreases, a gain of some amplitude coefficient ratio is increased to the highest degree, which means that the region where homoclinic intersection does not occur will be enlarged as much as possible, leading to the best possible control performance. Finally, it is shown that the theoretical analysis is in agreement with the numerical simulations on several concerned issues including the identification of the stable and unstable manifolds and the basins of attraction. © Springer 2005.

Research Area(s)

  • Duffing oscillator, Homoclinic bifurcation, Nonlinear oscillator, Optimal control, Periodic excitation

Citation Format(s)

A simplified optimal control method for homoclinic bifurcations. / Cao, Hongjun; Chen, Guanrong.
In: Nonlinear Dynamics, Vol. 42, No. 1, 10.2005, p. 43-61.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review