Synchronization of Time-Delay Chaotic Systems in the Presence of Parameters Uncertainties with Sliding Mode Observer Design

In secure communication applications, time delay chaotic systems are more confidential than the simple chaotic systems. Therefore, in this paper synchronization of time delay chaotic systems has been investigated. Sliding mode observer based approach has been applied as a synchronization method and the stability of the proposed observer has been guaranteed. In order to enhance the level of security of the communication system, the parameters of drive system (transmitter) are assumed to be unknown at the response system (receiver). These uncertainties lie in linear part of the system but sliding mode observer just compensates the uncertainties that lie in nonlinear parts, so the proposed sliding mode observer cannot retrieve the actual states correctly. The proposed solution is on-line identification of the uncertain parameters using the states which have been estimated by the observer. In order to identify the uncertain parameters, the model of the system must be rewritten linearly in terms of unknown parameters. Then the parameters are estimated using Recursive Least Squares (RLS) algorithm. The estimated arameters are used simultaneously in state estimation by the observer. Consequently, the synchronization performance is increased significantly. The result is illustrated numerically on the synchronization of chaotic time-delay Chua's circuit and the simulation results demonstrate the efficiency of the proposed scheme.