Control of limit cycle amplitude through non-smooth bifurcations

In this paper we present two methods for controlling limit cycles in smooth planar systems making use of the theory of nonsmooth bifurcations. They correspond to two novel switching control strategies for reducing the amplitude of undesired limit cycles in autonomous smooth systems. The switching controller is designed by using the theory of nonsmooth bifurcations. By designing an appropriate switching controller, the occurrence of a corner-sliding bifurcation or a grazing-sliding bifurcation is induced on the system and the amplitude of the target limit cycle is controlled. The switching control action is only started when the system trajectories enter an appropriately defined region in phase space. This technique is illustrated through a representative example.