Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems

This paper is concerned with a novel secure data transmission design based on adaptive synchronization of master and slave unified chaotic systems. First, by introducing an augmented error state, an adaptive continuous sliding mode control (SMC) is derived to guarantee the synchronization of unified chaotic systems. Then, the secret message embedded in the master chaotic system can be transmitted from transmitter to receiver. Different from previous works using discontinuous SMC, the undesired chattering phenomenon can be fully eliminated, and it becomes possible to precisely recover the embedded secret message at the receiver. Last, an example is given to illustrate the success of secure data transmission with the continuous SMC developed in this paper.

A Linear Matrix Inequality Approach to Output Feedback Control of Fractional-Order Unified Chaotic Systems With One Control Input

This paper focuses on stabilization of fractional-order unified chaotic systems. In contrast to existing methods in literature, the proposed method requires only the system output for feedback and uses only one control input. The controller consists of a state feedback control law and a dynamic estimator. Sufficient stability conditions are derived using a fractional-order extension of the Lyapunov direct method and a new lemma of the Caputo fractional derivative. The conditions are expressed in the form of linear matrix inequalities (LMIs). All the parameters of the controller can be simultaneously obtained by solving the LMIs. Numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed method.