Bifurcation placement of hopf points for stabilization of equilibria

Abstract:
Applications of bifurcation control to chemical engineering processes have aimed at rendering subcritical bifurcations supercritical. Beyond affecting the criticality of bifurcation points for control purposes, it is possible to deliberately introduce bifurcation points to stabilize parts of the equilibrium manifold of an ODE process model. This can be done without affecting the equilibrium manifold of the uncontrolled process. For brevity this approach is called bifurcation placement. The present paper focuses on the introduction of Hopf bifurcations, though the approach is more general. Conditions are stated for the introduction of a Hopf bifurcation at a given location on the equilibrium manifold of a system of ODEs. The proof is constructive in the sense that it allows to calculate the controller needed for the introduction of the desired bifurcation point. A simple motivating example and an application to a model of an industrial continuous polymerization process are presented.

Keywords:
Bifurcation control, Hopf, saddle-node, stability.

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