Doğrusal olmayan gözleyici tasarımı ve kaotik sistemlerin eşzamanlamasına uygulanması

ABSTRACT NONLINEAR OBSERVER DESIGN WITH APPLICATION TO THE SYNCHRONIZATION OF CHAOTIC SYSTEMS Ercan Solak M.S. in Electrical and Electronics Engineering Supervisor: Assoc. Prof. Dr. Ömer Morgül August 1996 Observers are used to estimate the states of dynamical systems whenever they are not available through direct measurements. Although the design of lin ear observers is a well-developed branch of control theory, its counterpart for nonlinear systems is a relatively new field. In this thesis, an observer construction methodology is proposed for a class of nonlinear systems satisfying certain conditions. Then, the problem of syn chronizing chaotic systems, which has found recent applications in the area of secure message transmission, is addressed from the observer design point of view. In the design, we exploited one of the essential properties of the chaotic systems that the trajectories remain in a bounded region of the state space. It is also shown that, for certain well-known chaotic systems, the system structure enables one to use linear observer schemes in order to have global synchroniza tion. Keywords : Nonlinear observers, chaotic systems, chaos synchronization. m