Synchronization in Networked Systems with Parameter Mismatch: Adaptive Decentralized and Distributed Controls

TL;DR

This paper develops adaptive decentralized and distributed control strategies to synchronize mismatched networked systems, ensuring bounded stability and convergence to desired trajectories, verified through simulations of Lorenz oscillators.

Contribution

It introduces novel adaptive control methods for mismatched networks, providing finite-time error bounds and asymptotic synchronization techniques.

Findings

Error norm boundedness achieved in finite time

Decentralized compensator successfully pins network to desired trajectory

Distributed estimators effectively handle parameter mismatches

Abstract

Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. We derive an upper bound on the norm of the error of network states from its average states, which it achieves in finite time. Then, we devise a decentralized compensator to asymptotically pin the network of mismatched systems to a desired trajectory. Next, we design distributed estimators to compensate for the mismatched parameters performances of adaptive decentralized and distributed compensations are analyzed. Our analytical results are verified by several simulations in a network of globally connected Lorenz oscillators.