Signal Transmission by Sampled-time Adaptive Synchronization of Time-varying Chaotic Systems

Abstract

In the paper, the adaptive synchronization problem is studied for a class of time-varying nonlinear systems. The only assumption imposed is the boundedness of the rate of change of the controlled system parameters, while the initial uncertainty can be quite large. The adaptation algorithms in the discrete-time form are derived based on adaptive control of nonlinear time-varying systems with an explicit reference model. As the result, the estimate of the limiting deviation of the solution of the closed-loop system from that of the reference model was obtained. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limiting error in the system can be made arbitrarily small despite a possibly big range of system parameter values. The systems based on a direct approach are considered. The procedure for the synthesis of a sampled-time adaptive controller and analysis of the synthesized system is illustrated by an example of the signal transmission system. The results obtained allow one to build and analyze a wide class of adaptive systems with reference models under time-varying conditions.