Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

Details Control of Integrable Hamiltonian Systems and Degenerate Bifurcations Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

2003-06-12

arxiv.org/abs/nlin/0306018v2

Nonlinear Sciences

Pattern Formation and Solitons

25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and referenc

Scientific paper

10.1103/PhysRevE.70.016205

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.

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