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Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

C. W. Kulp·E. R. Tracy
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Abstract

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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C. W. Kulp, E. R. Tracy. 2004-03-02. Control of Integrable Hamiltonian Systems and Degenerate Bifurcations. https://doi.org/10.1103/physreve.70.016205

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