Dynamic Average Consensus under Limited Control Authority and Privacy Requirements

TL;DR

This paper presents a continuous-time distributed algorithm for dynamic average consensus that accounts for limited control authority and privacy, with adjustable steady-state error and convergence properties.

Contribution

It introduces a novel consensus algorithm that ensures privacy, handles input saturation, and allows agents to control convergence rates, extending existing methods.

Findings

Algorithm achieves steady-state error control.

Preserves privacy of local inputs and transient states.

Handles input saturation and convergence rate control.

Abstract

This paper introduces a novel continuous-time dynamic average consensus algorithm for networks whose interaction is described by a strongly connected and weight-balanced directed graph. The proposed distributed algorithm allows agents to track the average of their dynamic inputs with some steady-state error whose size can be controlled using a design parameter. This steady-state error vanishes for special classes of input signals. We analyze the asymptotic correctness of the algorithm under time-varying interaction topologies and characterize the requirements on the stepsize for discrete-time implementations. We show that our algorithm naturally preserves the privacy of the local input of each agent. Building on this analysis, we synthesize an extension of the algorithm that allows individual agents to control their own rate of convergence towards agreement and handle saturation bounds on the driving command. Finally, we show that the proposed extension additionally preserves the privacy of the transient response of the agreement states and the final agreement value from internal and external adversaries. Numerical examples illustrate the results.