Controller parameters determination based on bifurcation structure of controlled system

The bifurcation properties of controlled chaotic systems on the Poincare section was investigated numerically, and the ranges of the main parameters, such as the control gain and the feedback time delay, were determined to design a controller for the control aim. According to the geometrical structure features of the chaotic attractor, an appropriate Poincare section was selected to reveal the bifurcation character of the controlled chaotic system. Three typical chaotic systems were taken as examples where different desired periodic states were attained by determining the range of controller parameters according to the bifurcation features of the controlled system. The simulation results of the typical controlled chaotic systems show the validity of the proposed method with both theoretical and practical significance.