Analysis of an adaptive hybrid control system which stabilizes unstable periodic orbits embedded in chaotic attractors

Abstract

In this paper, an adaptive hybrid control method is proposed, which stabilizes chaotic systems in the neighborhood of unstable periodic orbits embedded in the chaotic dynamics of the process to control. The method is based on the joint action of two controllers (a continuous time controller and a discrete time controller) as well as on the phenomenon of adaptive synchronization of the plant with an specified reference model. In some cases, the method only needs a partial driven reference model. An stability analysis of the control system is performed and an algorithtm is proposed to facilitate the implementation of the method. Finally, numerical simulation results are shown.

Keywords

• Control híbrido
• control adaptativo
• órbita periódica inestable
• modelo de referencia
• sincronización
• sistemas caóticos