Distributed multiple-bipartite consensus in networked Lagrangian systems with cooperative-competitive interactions

2021 ◽  
Author(s):  
Tiehui Zhang ◽  
Hengyu Li ◽  
Jun Liu ◽  
Daowei Lu ◽  
Shaorong Xie ◽  
...  
Keyword(s):  
Collective Behavior ◽  
Lagrangian Systems ◽  
Group Consensus ◽  
Consensus Control ◽  
Control Laws ◽  
Cluster Group ◽  
Competitive Network ◽  
Leader Following ◽  
Bipartite Consensus ◽  
Networked Lagrangian Systems

Abstract In combination with the collective behavior evolutions of bipartite consensus and cluster/group consensus, this paper proposes the notion of multiple-bipartite consensus in networked Lagrangian systems (NLSs). The distributed leaderless and leader-following multiple-bipartite consensus control laws for NLSs are presented in the cooperative-competitive network, where the negative interactions between agents can exist in the same subnetwork. By introducing an acyclic partition and adding the integral item in the control protocols, the final explicit convergence states in the leaderless case are eventually obtained. Moreover, the leader-following scenario can be realized in fifinite time with integrated controllers. All of the effectiveness has been illustrated through numerical simulations.

scholarly journals Leader-Following Regional Multiple-Bipartite Consensus for Networked Lagrangian Systems with Coopetition Interactions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 920
Author(s):  
Tiehui Zhang ◽  
Hengyu Li ◽  
Zhaoyan Wang ◽  
Shaorong Xie
Keyword(s):  
Auxiliary Variable ◽  
Cooperative Networks ◽  
Lagrangian Systems ◽  
Final States ◽  
Analysis Theory ◽  
Nonlinear Control Theory ◽  
Leader Following ◽  
Bipartite Consensus ◽  
The Stability ◽  
Networked Lagrangian Systems

This paper investigates the leader-following regional multiple-bipartite consensus problems of networked Lagrangian systems (NLSs) in coopetition networks. Our framework expands the application scopes of traditional regional consensus in cooperative networks. With the aid of a novel auxiliary variable embedded in the control protocols, the final states of NLSs are guaranteed to realise multi-regional symmetry in the constructed multiple symmetric regions. By utilising the characteristic of acyclic topology in the structurally balanced graph, the stability of the closed system is performed by perturbation analysis theory, nonlinear control theory, functional analysis theory, and so on. Finally, the effectiveness of our approach is verified by numerical simulations.

Distributed H∞ Control for Leader-Following Coordination with Switching Topology

2011 ◽  
Vol 135-136 ◽  
pp. 455-463
Author(s):  
Yan Ping Luo ◽  
Li Xin Gao
Keyword(s):  
Control Problem ◽  
External Disturbance ◽  
Switching Topology ◽  
Consensus Control ◽  
Common Lyapunov Function ◽  
Control Laws ◽  
Leader Following ◽  
Multi Agent ◽  
Feedback Laws ◽  
Parameter Dependent

In this paper, we consider multi-agent H∞consensus control problems with external disturbance under the undirected switching topologies. The agent dynamics is expressed in the form of a second-order model and the control laws are neighbor-based feedback laws. By using the model transformation, the multi-agent H∞consensus control problem is converted into H∞ control problem for a switching linear system with special structure. A sufficient condition is established under which all agents can reach consensus with the desired H∞performance in switching topology case by constructing a parameter-dependent common Lyapunov function. Moreover, we give an explicit estimation expression to estimate H∞ performance index. Finally, a numerical example is provided to illustrate the effectiveness of our results.

Bipartite Consensus Control for a Swarm of Robots

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Jun Liu ◽  
Hengyu Li ◽  
Jinchen Ji ◽  
Jun Luo
Keyword(s):  
Network Topology ◽  
Laplacian Matrix ◽  
Lagrangian System ◽  
Consensus Control ◽  
Lagrangian Equations ◽  
Competitive Network ◽  
Simulation Results ◽  
Bipartite Consensus ◽  
Virtual Leader ◽  
Theoretical Results

Abstract This paper studies the bipartite consensus problem of a swarm of robots whose dynamics are formulated by Lagrangian equations. Two distributed bipartite consensus control protocols are proposed for a swarm of robots without a leader or with a virtual leader. For the nonleader case, the networked Lagrangian system can reach static bipartite consensus under the control protocol developed, and the final convergent states can be explicitly determined by the specific structure of the Laplacian matrix associated with the cooperative–competitive network topology. For the virtual leader case, all the followers can track the leader's state in a bipartite formation to realize bipartite tracking consensus. Finally, the simulation results are given to verify the theoretical results.

Practical Bipartite Consensus for Networked Lagrangian Systems in Cooperation-Competition Networks

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Tiehui Zhang ◽  
Hengyu Li ◽  
Jun Liu ◽  
Huayan Pu ◽  
Shaorong Xie ◽  
...  
Keyword(s):  
Lagrangian Systems ◽  
Bipartite Consensus ◽  
Networked Lagrangian Systems
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