A computer-aided design method of stabilizing controllers for chaotic systems — External force control

Chaos occurs widely in artificial and natural nonlinear systems and its irregular behavior is 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 computer-aided design method of stabilizing controllers for continuous-time chaotic systems, in which we extend our previous work so as to realize better performance. It is known that infinitely many unstable periodic orbits are embedded in chaotic attractors. Therefore, finding an unstable periodic orbit out of them and designing a controller which stabilizes it, we can obtain a controller which makes the transition to the stable periodic orbit and suppresses chaotic behavior. With this in mind, we take two steps in order to design stabilizing controllers: (1) finding one of unstable periodic orbits imbedded in a chaotic attractor, and (2) designing a controller which stabilizes it. We propose a design method of feedback controllers which stabilize it by extending our previous method. The concept of so called external force control is introduced in order to achieve superior control performance and easier implementation. It is shown through experimental studies that the proposed method makes it possible to realize transitions from chaotic states to stable periodic states more easily and exactly.