Abstract
The paper is concerned with the consensus problem in a multi-agent system such that each agent has boundary constraints. Classical Olfati-Saber's consensus algorithm converges to the same value of the consensus variable, and all the agents reach the same value. These algorithms find an equality solution. However, what happens when this equality solution is out of the range of some of the agents? In this case, this solution is not adequate for the proposed problem. In this paper, we propose a new kind of algorithms called supportive consensus where some agents of the network can compensate for the lack of capacity of other agents to reach the average value, and so obtain an acceptable solution for the proposed problem. Supportive consensus finds an equity solution. In the rest of the paper, we define the supportive consensus, analyze and demonstrate the network's capacity to compensate out of boundaries agents, propose different supportive consensus algorithms, and finally, provide some simulations to show the performance of the proposed algorithms.
Highlights
This paper presents a novel approach to deal with consensus with bounded capacity nodes
Consensus problems consist of a group of entities that wants to reach an agreement about the value of a variable of interest in an incomplete information scenario
The supportive consensus algorithms that we introduce in this paper are similar to Olfati’s because they must keep the mean, and they must allow that some agents in the network can compensate the Δ(t), and obtaining satisfactory agreements for all of them
Summary
This paper presents a novel approach to deal with consensus with bounded capacity nodes. The approximate algorithms try to solve the problem by combining the consensus algorithm with a method that compensates values corresponding to agents that are ‘out of its boundaries’ in each iteration When these algorithms reach a stable state, a small amount of ‘out of boundaries values’ cannot be distributed in the network. For this reason, we have defined the relative error, which allows us to estimate the reliability of the solutions obtained. A second experiment studies how the error of the value reached concerning the mean of the initial values with each of the algorithms varies according to the network’s size This experiment shows how, as the network’s size increases, the error is distributed throughout the network, and the deviation from the desired value is small. We want to highlight that ‘supportive consensus’ is an open problem, and that other algorithms are possible
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