Dynamic feedback control of bifurcations

Bifurcation control deals with the modification of the bifurcation characteristics of a parameterized nonlinear system by a judiciously designed control input. We consider the problem of dynamic feedback control of bifurcations. In particular, previous results on the control of bifurcations using washout filters are extended to some general forms of dynamic feedback controllers. It is shown that high-pass filters such as washout filters can be represented by a special form of dynamic feedback controller. The control effect on bifurcations can be readily assessed by analytical formulae. These dynamic feedback controllers offer more flexibility over the original controller in bifurcation control. The results are viable for the design and analysis of nonlinear control systems involving bifurcations