Master-Slave Synchronization for Trajectory Tracking Error Using Time-Delay Recurrent Neural Networks via Krasovskii-Lur’e Functional for Chua’s Circuit

This paper presents an application of a time-delay neural networks to chaos synchronization. The two main methodologies, on which the approach is based, are time-delay recurrent neural networks and inverse optimal control for nonlinear systems. The problem of trajectory tracking is studied, based on the Lyapunov-Krasovskii and Lur'e theory, that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a reference function is obtained. The method is illustrated for the synchronization, the analytic results we present a trajectory tracking simulation of a time-delay dynamical network and the Chua's circuits.