PREDICTIVE POINCARE CONTROL - A CONTROL-THEORY FOR CHAOTIC SYSTEMS

One of the most interesting features of chaotic systems is the large n umber of unstable orbits embedded in a chaotic attractor. In this work , we propose a global chaos-control technique called predictive Poinca re control (PPC) that permits stabilization of a predefined solution, using only small control pulses. We prove this result for a large clas s of n-dimensional chaotic systems. The predefined solution can be a p eriodic or nonperiodic oscillation, expressed by a periodic or nonperi odic symbolic sequence [S. Hayes, C. Grebogi, and E. Ott, Phys. Rev. L ett. 70, 3031 (1993)]. We apply the general PPC scheme to the well kno wn Lorenz model and study its robustness with respect to parasitic eff ects.