Takuji Kousaka, Tetsushi Ueta, Hiroshi Kawakami, Chaos and Control of Periodically Switched Nonlinear Systems, CONICET and UNS, The Latin American Applied Research Journal, Vol.1, No.31, 211-218, July 2001.
Abstract: 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 Poincar sections should be naturally attached at these points and then the Poincar 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 Poincar map. The controlled system is fully described as the differentiable map, there fore the controller can be designed by using conventional pole assignment technique. As 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 or bits and chaotic attractors e clarified. We also investigate bifurcation structure of phase locked regions along a Neimark-Sacker bifurcation set. Some theoretical results are con firmed by laboratory experiments. Secondly we try to stabilize 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 Poincar map. The results of numerical simulations are demonstrated.