Dynamic Min and Max Consensus and Size Estimation of Anonymous Multiagent Networks

Abstract

In this paper we propose two distributed control protocols for discrete-time multi-agent systems (MAS), which solve the dynamic consensus problem on the max value. In this problem each agent is fed an exogenous reference signal and has the objective to estimate and track the instantaneous and time-varying value of the maximum among all the signals fed to the network by exploiting only local and anonymous interactions among the agents. The first protocol achieves bounded steady-state and tracking errors which can be traded-off for convergence time. The second protocol achieves zero steady-state error and requires knowledge of an upper bound to the diameter of the graph representing the network. Modified versions of both protocols are provided to solve the dual dynamic minconsensus problem. These protocols are then exploited to solve a distributed size estimation problem in a network of anonymous agents in a dynamic setting where the size of the network is time-varying during the execution of the estimation algorithm. Numerical simulations are provided in order to corroborate the characterization of the proposed protocols.

Distributed Asynchronous Greedy Control of Large Networks of Thermostatically Controlled Loads for Electric Demand Response

“…Thus, at least the ESP knows n and can send this information to the agents while preserving the privacy of their power consumption. In addition, even if n is not available for any reason, distributed network size estimation algorithms, such as [20], can be used to estimate n.…”

Novel Stability Conditions for Nonlinear Monotone Systems and Consensus in Multi-Agent Networks

“…It is easy to verify that discrete-time systems x(k + 1) = f (x(k)) ruled by a max-plus map are K-topical. Applications of max-plus maps arise in several fields, such as optimal control [49],decentralized estimation [50], discrete event systems [51], and many others.…”

An Adaptive Distributed Protocol for Finite-Time Infimum or Supremum Dynamic Consensus

“…Another important class of consensus problems is the min/max formulation, for which both a static and a dynamic version can be identified. In the static version, the objective is to achieve a consensus within the network towards the min (or max) of the agents initial conditions, see for example [5]- [8], while on the dynamic formulation the objective is to track the min (or max) over a set of exogenous signals, each owned by one agent, see for example [9].…”

“…In this paper, for the reasons mentioned above, we will focus our attention only on the infimum (or supremum) dynamic consensus problem. In this regard, to the best of the authors' knowledge, the only relevant reference is [9], where the authors address the dynamic min/max consensus by proposing a discrete-time protocol with convergence error bounds guarantees by assuming exogenous signals with known bounded derivatives. On the contrary, in our setting, each agent is assumed to have an exogenous time-varying signal with unknown bounded derivative.…”