Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints

TL;DR

This paper analyzes output feedback synchronization of nonlinear systems under communication constraints, proposing a binary coder-decoder scheme and demonstrating exponential error convergence at high transmission rates.

Contribution

It introduces a novel binary coding scheme and provides a theoretical framework for synchronized control of nonlinear systems with limited communication capacity.

Findings

Synchronization error exponentially tends to zero at high transmission rates

The approach extends to tracking problems with external reference signals

Application to chaotic Chua systems demonstrates practical effectiveness

Abstract

Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is described and a theoretical analysis for multi-dimensional master-slave systems represented in 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 synchronization error exponentially tends to zero for sufficiantly high transmission rate (channel capacity). The results obtained for synchronization problem can be extended to tracking problems in a straightforward manner, if the reference signal is described by an {external} ({exogenious}) state space model. The results are applied to controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.