Consensus and swarming behaviors for a proportional-derivative system with a cut-off interaction

2021 ◽  
Vol 69 (6) ◽  
pp. 472-484
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Simple Eigenvalue ◽  
Local Information ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Bounded Distance ◽  
Communication Topology ◽  
Derivative System ◽  
Multi Agent ◽  
Simulation Results

Abstract This paper presents a proportional-derivative protocol for the consensus problem of a class of linear second-order multi-agent systems with local information transmission. The communication topology among the agents is switching and agents receive information within a critical bounded distance. As new observations, we show that the desired protocol system undergoes consensus and swarming behaviours when 1 is a simple eigenvalue of the adjacency matrix. In this case, both final velocity and final relative position are formulated. Simulation results show the effectiveness of the proposed protocol.

scholarly journals Nonlinear Consensus Protocol Modified from Doubly Stochastic Quadratic Operators in Networks of Dynamic Agents

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1519 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sultan Almotairi ◽  
Hamad Almohamedh ◽  
Sherzod Turaev ◽  
Badr Almutairi
Keyword(s):  
Theoretical Analysis ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Agent Systems ◽  
Doubly Stochastic ◽  
Average Consensus ◽  
Multi Agent ◽  
Mathematical Equations ◽  
Simulation Results

This article explores nonlinear convergence to limit the effects of the consensus problem that usually occurs in multi-agent systems. Most of the existing research essentially considers the outline of linear protocols, using complex mathematical equations in various orders. In this work, however, we designed and developed an alternative nonlinear protocol based on simple and effective mathematical approaches. The designed protocol in this sense was modified from the Doubly Stochastic Quadratic Operators (DSQO) and was aimed at resolving consensus problems. Therefore, we called it Modified Doubly Stochastic Quadratic Operators (MDSQO). The protocol was derived in the context of coordinated systems to overcome the consensus issue related to multi-agent systems. In the process, we proved that by using the proposed nonlinear protocol, the consensus could be reached via a common agreement among the agents (average consensus) in a fast and easy fashion without losing any initial status. Moreover, the investigated nonlinear protocol of MDSQO realized the reaching consensus always as well as DSQO in some cases, which could not reach consensus. Finally, simulation results were given to prove the validity of the theoretical analysis.

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

2017 ◽  
Vol 40 (5) ◽  
pp. 1529-1537 ◽  
Author(s):  
Muhammad Iqbal ◽  
John Leth ◽  
Trung D Ngo
Keyword(s):  
Convergence Rate ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Cyclic Pursuit ◽  
Leader Following ◽  
Multi Agent ◽  
Simulation Results ◽  
Pursuit Strategy

In this paper, we solve the leader-following consensus problem using a hierarchical nearly cyclic pursuit (HNCP) strategy for multi-agent systems. We extend the nearly cyclic pursuit strategy and the two-layer HNCP to the generalized L-layer HNCP that enables the agents to rendezvous at a point dictated by a beacon. We prove that the convergence rate of the generalized L-layer HNCP for the leader-following consensus problem is faster than that of the nearly cyclic pursuit. Simulation results demonstrate the effectiveness of the proposed method.

Forced Consensus of Multi-Agent Systems with Directed Communication Topology and Interval Time-Varying Delay

2013 ◽  
Vol 321-324 ◽  
pp. 852-857
Author(s):  
Ming Kai He ◽  
Jun Wei Wang
Keyword(s):  
Stability Analysis ◽  
Reference Trajectory ◽  
Time Varying ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Time Varying Delay ◽  
Communication Topology ◽  
Multi Agent ◽  
Varying Delay

This paper is concernedwith forced consensus problem for directed multi-agent systems with intervaltime-varying delay, whereall agents approach a constant reference trajectory under the condition thatonly a subset of the agents can receive information from the reference state. Thetime-varying delay is assumed to belong to an interval with known lower andupper bounds, but its lower bound may be greater than zero. We first propose a consensusalgorithm that extends the existing results in the literature to account forinterval time-varying delay. Then, the consensus stability analysis isconducted by introducing an appropriate Lyapunov-Krasovskii functional and using Jensen inequalitytechnique. A delay-range-dependentstability criterion is derived in terms of linear matrixinequalities, which can be efficiently solved by the interior-point algorithm.Finally, simulation examples indicatethe capabilities of the proposed algorithm.

scholarly journals An overview of the consensus problem in the control of multi-agent systems

Automatika ◽  
2018 ◽  
Vol 59 (2) ◽  
pp. 143-157 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Shahrum Shah Abdullah ◽  
Sherzod Turaev ◽  
Mohamed Othman
Keyword(s):  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent

scholarly journals Linear and nonlinear stochastic distribution for consensus problem in multi-agent systems

2018 ◽  
Vol 32 (1) ◽  
pp. 261-277 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Shahrum Shah Abdullah ◽  
Sherzod Turaev ◽  
Akram Zeki ◽  
Imad Al-Shaikhli
Keyword(s):  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Linear And Nonlinear ◽  
Stochastic Distribution

Leader-following consensus of heterogeneous linear multi-agent systems: New results based on linear transformation method

2021 ◽  
pp. 014233122110582
Author(s):  
Yangzhou Chen ◽  
Guangyue Xu ◽  
Jingyuan Zhan
Keyword(s):  
Linear Transformation ◽  
Design Method ◽  
Transformation Method ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Agent Systems ◽  
Hurwitz Stability ◽  
Leader Following ◽  
Multi Agent

This paper studies the leader-following state consensus problem for heterogeneous linear multi-agent systems under fixed directed communication topologies. First, we propose a consensus protocol consisting of four parts for high-order multi-agent systems, in which different agents are allowed to have different gain matrices so as to increase the degree of design freedom. Then, we adopt a state linear transformation, which is constructed based on the incidence matrix of a directed spanning tree of the communication topology, to equivalently transform the state consensus problem into a partial variable stability problem. Meanwhile, the results of the partial variable stability theory are used to derive a sufficient and necessary consensus criterion, expressed as the Hurwitz stability of a real matrix. Then, this criterion is further expressed as a bilinear matrix inequality condition, and, based on this condition, an iterative algorithm is proposed to find the gain matrices of the protocol. Finally, numerical examples are provided to verify the effectiveness of the proposed protocol design method.

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