Control and synchronization of fractional order non linear dynamical systems

Abstract

In real world systems, controlling the system so as to achieve desired performance is one of the fundamental objectives of design. Many control strategies have been developed over the years to analyse stability and synchronization of integer order linear and nonlinear systems. Extension of different traditional approaches to control and synchronize the fractional order nonlinear dynamical systems, is the main motivation for the work presented in this thesis. Here, fractional order version of Lyapunov stability theory is presented and employed as basis for use of traditional control approaches such as backstepping control, active control and active backstepping control, which are further used for control and synchronization of fractional order chaotic systems. newline newlineControl and synchronization using backstepping approach is obtained for fractional order systems belonging to strict feedback class. The systems with knownparameters as well as unknown parameters are handled here. Further, active backstepping technique, which incorporates the advantages of active control and backstepping approach, is employed to address control and synchronization of fractional order chaotic systems falling in a more general class. For discrete version of fractional order chaotic systems, active control technique is used for control and synchronization. Along with that, chaotic behaviour of fractional order generalized Henon map is also analysed here. newline newlineThe application of chaos synchronization of fractional order chaotic system is employed to address the problem of secure communication, where a speech signal is masked with a chaotic signal for transmission. The message signal can be recovered by newlineutilizing a backstepping based synchronizing controller following the reverse of the process followed at transmitter end. This scheme is further extended for encryption and transmission of a grayscale image. newlineand#8195; newlineFundamentals related to realization of fractional order systems are described in the last part of the thesis. Some of the systems which are u