Controlled Synchronization Under Information Constraints

TL;DR

This paper analyzes controlled synchronization under limited information capacity, proposing a simple coding scheme and deriving bounds on synchronization error related to channel capacity, with applications to chaotic systems.

Contribution

It extends existing frameworks to controlled master-slave synchronization with limited communication, providing a theoretical analysis and practical coding scheme.

Findings

Synchronization error bounds are proportional to transmission error.

Error bounds are inversely proportional to channel capacity.

Application to chaotic Chua systems demonstrates practical relevance.

Abstract

The class of controlled synchronization systems under information constraints imposed by limited information capacity of the coupling channel is analyzed. It is shown that the framework proposed in A. L. Fradkov, B. Andrievsky, R. J. Evans, Physical Review E 73, 066209 (2006) is suitable not only for observer-based synchronization but also for controlled master-slave synchronization via communication channel with limited information capacity. A simple first order coder-decoder scheme is proposed and a theoretical analysis for multi-dimensional master-slave systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification theorem. It is shown that the upper bound of the limit synchronization error is proportional to the upper bound of the transmission error. As a consequence, both upper and lower bounds of limit synchronization error are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). The results are applied to controlled synchronization of two chaotic Chua systems coupled via a controller and a channel with limited capacity.