PROBABILISTIC CONTROL OF CHAOS - CHAOTIC MAPS UNDER CONTROL

Recently, we have proposed a new probabilistic method for the control of chaotic systems [1]. In this paper, we apply our method to characte ristic cases of chaotic maps (one-and two-dimensional examples). As th ese chaotic maps are structurally stable, they cannot be controlled us ing conventional control methods without significant change of the dyn amics. Our method consists in the probabilistic coupling of the origin al system with a controlling system. This coupling can be understood a s a feedback control. of probabilistic nature. The chosen periodic orb it of the original system is a global attractor for the probability de nsities. The generalized spectral decomposition of the associated Frob enius-Perron operator provides a spectral condition of controllability for chaotic dynamical systems.