Contrôle des systèmes dynamiques chaotiques.

Abstract

The mathematical theory of control has undergone a very important development and its scope currently covers many fields, including industry, economics and biology. . . This thesis deals with the study of the control of chaotic dynamical systems. The latter constitute a particular class of nonlinear systems and are characterized by dynamic behaviors that are very sensitive to variations in the initial conditions. A method has been proposed for studying the stability of the fixed-point chaotic system, based on the Routh-Hurwitz criterion. In the first part, we presented the different tools presenting the chaotic behavior of the systems, and the main methods proposed in the literature for the study of the stability of dynamic systems with chaotic behavior; Lyapunov's method and the Routh-Hurwitz method. Finally we presented the main methods proposed in the literature for the control of the chaotic system. In the second part, we made a theoretical and numerical application of chaos control on some chaotic systems. The Routh-Hurwitz criterion is used, and the modified conditions, in addition Lyapunov's function to arrive at the control of the chaotic systems.