Consensus with Output Saturations

TL;DR

This paper analyzes the impact of output saturations on consensus algorithms, establishing precise initial conditions for achieving consensus in various agent models and graph structures.

Contribution

It provides necessary and sufficient initial state conditions for consensus under output saturations across different agent dynamics and graph types.

Findings

Consensus achieved if initial average is within saturation limits

Derived conditions for single and double-integrator agents

Extended results to directed graphs with weighted averages

Abstract

This paper consider a standard consensus algorithm under output saturations. In the presence of output saturations, global consensus can not be realized due to the existence of stable, unachievable equilibrium points for the consensus. Therefore, this paper investigates necessary and sufficient initial conditions for the achievement of consensus, that is an exact domain of attraction. Specifically, this paper considers singe-integrator agents with both fixed and time-varying undirected graphs, as well as double-integrator agents with fixed undirected graph. Then, we derive that the consensus will be achieved if and only if the average of the initial states (only velocities for double-integrator agents with homogeneous saturation levels for the outputs) is within the minimum saturation level. An extension to the case of fixed directed graph is also provided in which an weighted average is required to be within the minimum saturation limit.