A Design Method of Stabilizing Controllers for Chaotic Systems

Chaos occurs widely in artificial and natural nonlinear systems. Its irregular behavior is unpredictable and usually undesirable. Controlling chaos, that is, stabilization of chaotic systems, is one of major subjects in nonlinear control problems. In this paper we propose a design method of stabilizing controllers for continuous-time chaotic systems. It is well known that infinitely many unstable periodic orbits are embedded within chaotic attractors. Finding an unstable periodic orbit out of them and stabilizing it enable to make chaotic behavior transit to the stable periodic orbit. Firstly we discuss a method for finding an unstable periodic orbit in a chaotic attractor. Secondly we propose a design method of feedback controllers which stabilize it. Finally the validity of the proposed method is shown by performing numerical experiments.