Topology design for group consensus in directed multi-agent systems

Abstract

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GraParT: A MATLAB Toolbox for Partitioning Directed Graphs

“…Note that for a multi-agent network with dynamics given in Equation 1 (or equivalently Equation 4for discrete-time networks), the number of groups is related to the structure of the network [9][10][11][12]16]. The following lemma states relationship between the number of groups and the graph partitioning based on Definition 1.…”

“…Consider a network of 14 agents whose edge set is given by 𝐸 1 = {(𝑣 1 , 𝑣 2 ), (𝑣 1 , 𝑣 3 ), (𝑣 2 , 𝑣 3 ), (𝑣 3 , 𝑣 2 ), (𝑣 3 , 𝑣 9 ), (𝑣 3 , 𝑣 11 ), (𝑣 4 , 𝑣 5 ), (𝑣 5 , 𝑣 6 ), (𝑣 5 , 𝑣 7 ), (𝑣 6 , 𝑣 7 ), (𝑣 7 , 𝑣 4 ), (𝑣 7 , 𝑣 5 ), (𝑣 7 , 𝑣 11 ), (𝑣 8 , 𝑣 9 ), (𝑣 8 , 𝑣 14 ), (𝑣 9 , 𝑣 10 ), (𝑣 10 , 𝑣 11 ), (𝑣 10 , 𝑣 14 ), (𝑣 11 , 𝑣 12 ), (𝑣 11 , 𝑣 14 ), (𝑣 12 , 𝑣 13 ), (𝑣 12 , 𝑣 14 ), (𝑣 13 , 𝑣 12 )}. (12) Since there is no spanning tree in the graph 𝑮 𝟏 = (𝑽 𝟏 , 𝑬 𝟏 ), multiple groups will be formed in the network. Once the directed edges are entered as inputs to GraParT, Figure 2 illustrates the network graph, the reduced graph; the PLS and SLS of 𝑮 𝟏 , and evolutions of the states of the agents as functions of time.…”

“…The concepts of primary layer subgraphs (PLS) and secondary layer subgraphs (SLS), which were first introduced in [9], have been instrumental in our understanding of the grouping behavior of a multi-agent system. Once these subgraphs are determined, the topology designer can merge or divide the groups by adding new edges to the graph [12].…”

Stability analysis and controller design for consensus in discrete‐time networks with heterogeneous agent dynamics

“…In the last two decades, multi-agent systems (MASs) have received substantial research attention in a variety of fields including sensor networks [1], computer networks [2], clock synchronization [3], distributed decision making [4], distributed optimization [5], social networks [6], load balancing in power systems [7], formation-containment control [8,9], persistent monitoring [10], and robotics [11,12]. The consensus problem was investigated for the networks with first-order [13][14][15][16] and second-order agent dynamics [17][18][19][20] extensively. However, the agents in the distributed network may not have the same dynamics in practical applications [21].…”