Daisuke Ito, Tetsushi Ueta, Takuji Kousaka, Jun'ichi Imura, Kazuyuki Aihara, Controlling chaos of hybrid systems by variable threshold values, World Scientific, International Journal of Bifurcation and Chaos, Vol.24, No.10, pp.1450125-1-1450125-12, Oct. 2014.
Abstract: We try to stabilize unstable periodic orbits embedded in the given chaotic hybrid dynamical system by perturbation of a threshold value. In the conventional chaos control methods, a control input is designed by state-feedback value which is proportional to the difference between the target orbit and the current state, and it is applied into the specific system parameter as a small perturbation. During transition state, the control system consumes a certain control energy given by integration of such perturbations. In our method, we changes the threshold value dynamically to control the chaotic orbit. Unlike OGY method or the delayed feedback control, no actual control input is added into the system. The state-feedback is utilized only to determine the dynamic threshold value, thus the orbit starting from the current threshold value reaches the next controlled threshold value without any control energy. We obtain the variation of the threshold value from the composite Poincare map, and the controller is designed by the linear feedback theory with this variation. We demonstrate this method in simple hybrid chaotic systems and show performances with evaluating basins of attractions.