Anti-control of Hopf bifurcations through washout filters

Bifurcation control generally means to design a controller that can modify the bifurcation characteristics of a bifurcating nonlinear system, thereby achieving some desirable dynamical behaviors. A typical objective is delay and/or stabilization of a given bifurcation. In this paper, we consider the problem of anti-control of bifurcations, that is, a certain bifurcation is created with desired location and properties by appropriate controls. In particular, washout filter-aided dynamic feedback control laws are given for the creation of Hopf bifurcations. As Hopf bifurcations give rise to limit cycles, anti-control of Hopf bifurcations can be viewed as one approach to design limit cycles and nonlinear oscillations into a system via feedback control when such dynamical behaviors are desirable.