Adaptive Observer-based Synchronization of Nonlinear Nonpassifiable Systems

TL;DR

This paper introduces an adaptive observer-based synchronization method for nonlinear nonpassifiable systems, overcoming relative degree limitations and ensuring robustness and convergence in chaotic Lorenz system applications.

Contribution

It extends adaptive synchronization schemes to nonpassifiable systems using modern nonlinear control theory and new adaptation algorithms.

Findings

Achieved synchronization of chaotic Lorenz systems.

Proved parametric convergence in noiseless conditions.

Demonstrated robustness to measurement errors.

Abstract

The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive observer and high-order tuners. The solution is based on modern theory of nonlinear adaptive control, particularly on nonlinear observer structure and new classes of adaptation algorithms. Conditions of parametric convergence of the parameter estimation are established for the noiseless case. Robustness of the scheme to the bounded measurement error is established. The results are illustrated by example of application the proposed adaptive synchronization of chaotic Lorenz systems.