Chaos and control of periodically switched nonlinear systems

This paper discusses chaos and its control in periodically switched nonlinear systems. Since the trajectory of the system. Is not differentiable at break points, the Poincare sections should be naturally attached at these points and then the Poincare mapping is derived as a composite of local mappings defined among these sections. This map enable us to calculate the location and its stabilities of the periodic points in the chaotic attractor. We also consider chaos control problem based on the Poincare map. The controlled system is fully described as the differentiable map, therefore the controller can be designed by using conventional pole assignment technique. las an illustrated example, we consider a Rayleigh type oscillator containing a periodic switch. We firstly discuss bifurcation sets of the system. The dynamic properties of periodic orbits and chaotic attractors are clarified. We also investigate bifurcation structure of phase-locked regions along a Neimark-Sacker bifurcation;ion set. Some theoretical results are confirmed by laboratory experiments, Secondly we try to stabilise one and two-period unstable periodic orbits by using the proposed method. The controller is calculated easily because all information can be obtained from the Poincare map. The results of numerical simulations are demonstrated.