Tetsushi Ueta, Hiroshi Kawakami, Composite dynamical system for controlling chaos, Institute of Electronics, Information and Communication Engineers, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E78-A, No.6, 708-714, June 1995.
Abstract: We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincare mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C^0. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to . escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.