Output‐Feedback Controller Based Projective Lag‐Synchronization of Uncertain Chaotic Systems in the Presence of Input Nonlinearities

Abstract

This paper solves the problem of projective lag-synchronization based on output-feedback control for chaotic drive-response systems with input dead-zone and sector nonlinearities. This class of the drive-response systems is assumed in Brunovsky form but with unavailable states and unknown dynamics. To effectively deal with both dead-zone and sector nonlinearities, the proposed controller is designed in a variable-structure framework. To online learn the uncertain dynamics, adaptive fuzzy systems are used. And to estimate the unavailable states, a simple synchronization error is constructed. To prove the stability of the overall closed-loop system (controller, observer, and drive-response system) and to design the adaptation laws, a Lyapunov theory and strictly positive real (SPR) approach are exploited. Finally, three academic examples are given to show the effectiveness of this proposed lag-synchronization scheme.

Outer Synchronization of a Modified Quorum-Sensing Network via Adaptive Control

“…The former can be employed to discuss local stability of the synchronous state, and the latter can be used to explore global stability of the synchronous state. Up to now, dozens of different types of synchronization states have been proposed such as complete synchronization [14], cluster synchronization [15,16], lag synchronization [17,18], projection synchronization [19,20], and outer synchronization [21][22][23]. Thereinto, outer synchronization has attracted many researchers' interest, which describes the synchronization 2 Mathematical Problems in Engineering between two or more networks.…”