Distributed Average Tracking for Multiple Signals Generated by Linear Dynamical Systems: An Edge-based Framework

TL;DR

This paper introduces edge-based algorithms for distributed average tracking of multiple signals generated by linear systems, ensuring asymptotic or bounded convergence without chattering, applicable in networked control scenarios.

Contribution

It proposes novel static and adaptive edge-based algorithms for distributed average tracking of linear system signals, improving convergence properties and eliminating chattering.

Findings

Algorithms achieve asymptotic tracking without chattering.

Adaptive algorithms ensure bounded tracking errors with exponential convergence.

Simulation confirms theoretical effectiveness.

Abstract

This paper studies the distributed average tracking problem for multiple time-varying signals generated by linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In the edge-based framework, a pair of continuous algorithms with, respectively, static and adaptive coupling strengths are designed. Based on the boundary layer concept, the proposed continuous algorithm with static coupling strengths can asymptotically track the average of multiple reference signals without the chattering phenomenon. Furthermore, for the case of algorithms with adaptive coupling strengths, average tracking errors are uniformly ultimately bounded and exponentially converge to a small adjustable bounded set. Finally, a simulation example is presented to show the validity of theoretical results.