On control of planar periodic orbits

We investigate methods of reducing the size of large limit cycles using control in the case of limited actuator authority. We consider a planar nonlinear oscillatory system with bounded control. It is shown that under weak assumptions one can identify the controller that shrinks the existing limit cycles and maximizes the domain of attraction of the origin. Away from a small neighborhood of the origin, the optimal control action results in switching between the positive and negative saturation values. We illustrate the results of the paper showing how the throttle control can reduce the size of a surge limit cycle using the Greitzer compressor surge model.