Stability of Open Multi-Agent Systems and Applications to Dynamic Consensus

Mauro Franceschelli (1) , Paolo Frasca (2)

1 DIEE - Department of Electrical and Electronic Engineering [University of Cagliari]
2 DANCE - Dynamics and Control of Networks

In this technical note we consider a class of multi-agent network systems that we refer to as Open Multi-Agent Systems (OMAS): in these multi-agent systems, an indefinite number of agents may join or leave the network at any time. Focusing on discrete-time evolutions of scalar agents, we provide a novel theoretical framework to study the dynamical properties of OMAS. Specifically, we propose a suitable notion of stability and derive sufficient conditions for it. Our analysis regards the arrival/departure of agents as a disturbance; consistently, our stability conditions require the effect of arrivals/departures to be bounded (in a precise sense) and the OMAS to be contractive in the absence of arrivals/departures. In order to provide an example of application for this theory, we re-formulate the well-known Proportional Dynamic Consensus for Open Multi-Agent Systems and we study the stability properties of the resulting Open Proportional Dynamic Consensus algorithm.

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Mauro Franceschelli, Paolo Frasca. Stability of Open Multi-Agent Systems and Applications to Dynamic Consensus. IEEE Transactions on Automatic Control, 2021, 66 (5), pp.2326-2331. ⟨10.1109/TAC.2020.3009364⟩. ⟨hal-03291531⟩