Bipartite containment tracking of signed networks

Meng, Deyuan

doi:10.1016/j.automatica.2017.01.044

Cited by 148 publications

(68 citation statements)

References 24 publications

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“…From [21], we give the following definition of containment in signed graphs. Let us denote by L the set of nodes directly controlled by the leaders, that is,…”

Section: Problem Formulationmentioning

confidence: 99%

“…These results were later extended to the case of non-strongly connected graphs and discrete-time dynamics [16]- [20]. Recently, a first definition of containment control over signed graphs was given in [21]. Specifically, the author says that a network is contained when the states of its nodes converge towards the convex hull spanned by the leaders and by their symmetric trajectories.…”

Section: Introductionmentioning

confidence: 99%

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Partial containment control over signed graphs

DeLellis

DiMeglio

Garofalo

et al. 2019

2019 18th European Control Conference (ECC)

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In this paper, we deal with the containment control problem in presence of antagonistic interactions. In particular, we focus on the cases in which it is not possible to contain the entire network due to a constrained number of control signals. In this scenario, we study the problem of selecting the nodes where control signals have to be injected to maximize the number of contained nodes. Leveraging graph condensations, we find a suboptimal and computationally efficient solution to this problem, which can be implemented by solving an integer linear problem. The effectiveness of the selection strategy is illustrated through representative simulations. Achieving consensus is not the only possible control goal in multi-agent systems. Indeed, in applications of networks of autonomous agents, the objective is often to contain a group of agents within a certain area, e.g. not to enter populated areas. Motivated by that, Ji and coworkers introduced the socalled containment control problem, where multiple leaders have to drive a group of mobile agents within a desired convex polytope [5]. Later works have further analyzed this problem to account for the presence of directed interactions [6], possible switches in the network topology [7], [8], uncertainty [9], and higher-order dynamics [10], [11]. As noted by Altafini in [12], most of the works on consensus and containment control relies on the assumption of cooperation among the agents in the system, as all the network edges are assumed to have positive weights. However, in social network theory, besides cooperative interactions, also antagonism is commonly observed [13], [14]. A natural setting to describe such interactions is to characterize the network topology through the so-called signed graphs, introduced in the Fifties by Harary [15] to model the disliking, indifference, and liking sentiments described by psychologists in social interactions. These considerations motivated a

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“…From [21], we give the following definition of containment in signed graphs. Let us denote by L the set of nodes directly controlled by the leaders, that is,…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Partial containment control over signed graphs

DeLellis

DiMeglio

Garofalo

et al. 2019

2019 18th European Control Conference (ECC)

View full text Add to dashboard Cite

show abstract

“…To date, the coordination control of nonlinear signed networks has not received enough attention. Note that the signed networks in most of current works [25][26][27][28][29][30][31][32][33] are assumed to be composed by identical linear systems. In recent years, some attention has been paid to the coordination control of signed networks with nonlinear dynamics: Hu et al 47 considered the traditional synchronization problem for signed networks with Lipschitz-type node dynamics; Zhai et al [48][49][50] studied the bipartite leaderless and leader-following synchronization in a network of nonlinear systems satisfying the one-sided Lipschitz condition.…”

Section: Main Motivationsmentioning

confidence: 99%

“…To extend the results of first‐order signed networks, some researchers considered the bipartite consensus of signed networks with more general agent dynamics: Hu and Zhu considered the bipartite leader‐following consensus of multiagent systems with second‐order dynamics; Valcher and Misra discussed the bipartite consensus of high‐order multiagent systems; Zhang and Chen studied the bipartite consensus problem for multiagent systems with general linear dynamics based on state‐ and output‐feedback control approaches. In recent years, other types of collective behaviors of signed networks have also been investigated: Fan et al considered the bipartite flocking of second‐order multiagent systems under signed graphs; Meng addressed the bipartite containment control of signed networks with multiple leaders.…”

Section: Introductionmentioning

confidence: 99%

Bipartite synchronization of Lur'e network under signed digraph

Liu

Song

Wen

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper considers the bipartite leaderless and leader‐following synchronization in a network of coupled Lur'e systems with sector‐condition node dynamics and signed digraph topology, where the interaction digraph consists of both positive and negative communication links. Continuous‐time and sampled‐data control algorithms are, respectively, proposed to solve the bipartite synchronization problems for the signed Lur'e network. Under some assumptions on the network structure and node functions, some bipartite synchronization conditions are established for signed Lur'e network by using coordinate transform, linear matrix inequalities, and algebraic graph theories. For the continuous‐time control algorithms, it is shown that the bipartite synchronization problems of the signed Lur'e network can always be solved if the coupling strength is sufficiently large and the network topology satisfies some suitable conditions. For the sampled‐data control algorithms, an upper bound of the sampling intervals is estimated to ensure that the bipartite synchronization can be reached in the signed Lur'e network. Some simulation results are given to illustrate the effectiveness of the theoretical analysis.

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“…In recent years, multi-agent systems have great potential of application in the fields of biology, engineering, physics, society and so on. Also its distributed cooperative control [1,2] has attracted more and more researchers' attention. For example, the controllability [3][4][5][6][7][8][9][10][11] and the consensus problem [12][13][14][15][16][17][18][19] are widely studied in multi-agent systems.…”

Section: Introductionmentioning

confidence: 99%

Event-Based Consensus for General Linear Multiagent Systems under Switching Topologies

Sun

Liu

2020

Complexity

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In this paper, event-triggered leader-following consensus of general linear multiagent systems under both fixed topology and switching topologies is studied. First, centralised and decentralised event-triggered control strategies based on neighbors' state estimation are proposed under fixed topology, in which the controller is only updated at the time of triggering. Obviously, compared with the continuous time control algorithms, the event-triggered control strategies can reduce the communication frequency among agents effectively. Meanwhile, event-triggering conditions are derived for systems to achieve consensus by using the Lyapunov stability theory and model transformation method. en, the theoretical results obtained under the fixed topology are extended to the switching topologies, and the sufficient conditions for the system to achieve leader-following consensus under the switching topologies are given. However, different from fixed topology, the control input of each agent is updated both at event-triggering and topology switching time. Finally, Zeno behaviors can be excluded by proving that the minimum triggering interval of each agent is strictly positive, and the effectiveness of the event-triggered protocol is verified by simulation experiments.

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Bipartite containment tracking of signed networks

Cited by 148 publications

References 24 publications

Partial containment control over signed graphs

Partial containment control over signed graphs

Bipartite synchronization of Lur'e network under signed digraph

Event-Based Consensus for General Linear Multiagent Systems under Switching Topologies

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