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Published on: November 24, 2021
Control of integrable Hamiltonian systems and degenerate bifurcations
1Physics Department, College of William & Mary, Williamsburg, Virginia 23187-8795, USA.
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 bifurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrödinger equation.
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