Suppression of bursting

Suppression of bursting We investigate the possibility of using a single small amplitude control input and feedback to stabilize equilibrium sets in a class of highly nonlinear O (2) symmetric dynamical systems possessing structurally stable heteroclinic cycles. The leading-order behavior near the equilibria is bilinear and homogeneous in the state variables, while nonlinearities representing the symmetry breaking effect of the controller are crucial. After a series of simplifying transformations, we use ideas from optimal control theory to construct a stabilizing controller. This study is motivated by the desire to stabilize the burst/sweep cycle in low-dimensional models of a turbulent boundary layer. In the last two sections, we apply the techniques to the 10-dimensional system of Aubry et al . (1988). kw)Bilinear systems; dynamical systems; heteroclinic cycles; normal forms; optimal control; symmetry http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatica Elsevier

Suppression of bursting

Automatica, Volume 33 (1) – Jan 1, 1997

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Publisher
Elsevier
Copyright
Copyright © 1997 Elsevier Ltd
ISSN
0005-1098
D.O.I.
10.1016/S0005-1098(96)00137-9
Publisher site
See Article on Publisher Site

Abstract

We investigate the possibility of using a single small amplitude control input and feedback to stabilize equilibrium sets in a class of highly nonlinear O (2) symmetric dynamical systems possessing structurally stable heteroclinic cycles. The leading-order behavior near the equilibria is bilinear and homogeneous in the state variables, while nonlinearities representing the symmetry breaking effect of the controller are crucial. After a series of simplifying transformations, we use ideas from optimal control theory to construct a stabilizing controller. This study is motivated by the desire to stabilize the burst/sweep cycle in low-dimensional models of a turbulent boundary layer. In the last two sections, we apply the techniques to the 10-dimensional system of Aubry et al . (1988). kw)Bilinear systems; dynamical systems; heteroclinic cycles; normal forms; optimal control; symmetry

Journal

AutomaticaElsevier

Published: Jan 1, 1997

References

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