Group Consensus Of Multi-agent Systems Research Articles

Pinning Group Consensus of Multi-agent Systems Under DoS Attacks

In this paper, group consensus is investigated for a class of nonlinear multi-agent systems suffered from the DoS attacks. Firstly, a first-order nonlinear multi-agent system is constructed, which is divided into M subsystems and each subsystem has an unique leader. Then a protocol is proposed and a Lyapunov function candidate is chosen. By means of the stability theory, a sufficient criterion, which involves the duration of DoS attacks, coupling strength and control gain, is obtained for achieving group consensus in first-order system. That is, the nodes in each subsystem can track the leader of that group. Furthermore, the result is extended to nonlinear second-order multi-agent systems and the controller is also improved to obtain sufficient conditions for group consensus. Additionally, the lower bounds of the coupling strength and average interval of DoS attacks can be determined from the obtained sufficient conditions. Finally, several numerical simulations are presented to explain the effectiveness of the proposed controllers and the derived theoretical results.

Group consensus of multi-agent systems with hybrid characteristics and directed topological networks

In this paper, the group consensus problem is investigated for multi-agent systems (MASs) with hybrid characteristics and directed topological networks. Firstly, the dynamical model of hybrid multi-agent system (MAS) is constructed, which includes discrete time agents and continuous time agents. A class of distributed control protocols are put forward for hybrid MASs. Then, under fixed and directed topological networks, sufficient and necessary conditions for the realization of group consensus are provided on basis of matrix theory and graph theory. Finally, simulations examples are given to further verify the validity of our theoretical results.

Complex group consensus of multi-agent systems with cooperative-competitive mechanisms: acyclic partition method

For multi-agent system(MAS) with cooperative-competitive mechanisms, we aim to investigate its complex group consensus such as group scaled consensus and group-bipartite scaled consensus. Firstly, for directed graph G with m closed strongly connected components (CSCCs), we show the existence and nonuniqueness of its acyclic partition by giving a CSCC-based acyclic partition strategy, where MAS is divided into m subnetworks with directed spanning trees and the condensed graph of G is a directed acyclic graph. Secondly, under the extensive in-degree balance condition for cooperative-competitive network, an appropriate distributed control protocol is designed to guarantee that MASs can achieve group/group-bipartite scaled consensus by introducing cooperative-competitive matrix and scaling parameter matrix. Furthermore, to guarantee the faster convergence of MASs, we further improve and optimize the acyclic partition strategy by rich algebra and graph theories in three aspects: the selection of sub-root nodes, the division of multi-reachable nodes and the selection of directed spanning tree in each subnetwork. Finally, some simulation examples are presented to verify the effectiveness of our results.

Group consensus of multi-agent systems with additive noises

Group consensus of multi-agent systems with additive noises

Adaptive event-triggered group consensus of multi-agent systems with non-identical nonlinear dynamics

The paper is concerned with mean-square group consensus for second-order multi-agent systems with non-identical dynamics, where the agents in the same group have the identical dynamics, the agents in the different groups have non-identical nonlinear dynamics. To reduce the update frequency of event-triggered controller, a novel adaptive dynamic event-triggered communication scheme is presented based on the local stochastic sampled information. The proposed event-triggered conditions of the position state and velocity state have be given separately owe to their state ranges may be different, which lead to the position state and velocity state with different event-triggered instants and release intervals. The event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered conditions, the given event-triggered conditions are detected only at discrete sampled times, which means Zeno behavior can be excluded. A novel distributed protocol is designed based on the neighboring agents information of the position state and velocity state at event-triggered instants. The group consensus issue can be transformed into the convergence problem of the augmented error system. Then some mean-square group consensus criteria can be derived with the help of tools from graph theory and matrix analysis, and the event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the proposed transmission scheme.

Adaptive event-triggered group consensus of multi-agent systems under stochastic sampling

This paper investigates group consensus for linear multi-agent systems with nonidentical dynamics. A novel adaptive event-triggered communication scheme is presented by using the stochastic sampling information, the event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered condition, where event-triggered parameters can be adjusted with the system dynamics evolving. The group consensus protocol is designed based on the neighboring agents information at event-triggered instants, then a new stochastic sampled-data dependent error model is constructed, some group consensus criteria in mean-square can be derived and the feedback matrices can also be obtained. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Projective Group Consensus of Multi-Agent Systems with Arbitrary Parameter

In this paper, the projective group consensus issue for second order multi-agent systems (MASs) in directed graphs with a dynamic leader is investigated. The proposed projective group consensus with arbitrary parameter includes traditional consensus, reverse group consensus and cluster consensus as its special cases. Novel distributed control protocols are designed to obtain projective group consensus without analyzing signed directed graph as in most current literatures on bipartite consensus problem. On the basis of Lyapunov stability property, algebraic graph and some necessary matrix theory, sufficient conditions for delay and delay-free cases are derived. Finally, simulations of nonlinear chaotic MASs are adopted to testify the theoretical results.

Group consensus of multi-agent systems with cooperative-competitive interaction and communication delay in switching topologies networks based on the delta operator method

In this paper, group consensus of multi-agent systems with cooperative-competitive interaction and communication delay is investigated in switching topologies networks. The delta operator method and linear matrix inequality technique are used to establish the criteria on group consensus of this system. Combined with the stability theory, some sufficient conditions are given to guard the success of the group consensus of the multi-agent systems with switching topologies. Using this method, the problem of group consensus can be transformed into determining the globally asymptotically stable of a system with communication delay. The results can be applied to two situations on faults and communication delay without meeting the in-degree balance condition or spanning tree of part topologies. Several numeric simulations are given to illustrate the effectiveness of the theoretical results.

Group consensus of multi-agent systems subjected to cyber-attacks**Project supported by the National Natural Science Foundation of China (Grant Nos. 61807016 and 61772013) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181342).

In this paper, we investigate the group consensus for leaderless multi-agent systems. The group consensus protocol based on the position information from neighboring agents is designed. The network may be subjected to frequent cyber-attacks, which is close to an actual case. The cyber-attacks are assumed to be recoverable. By utilizing algebraic graph theory, linear matrix inequality (LMI) and Lyapunov stability theory, the multi-agent systems can achieve group consensus under the proposed control protocol. The sufficient conditions of the group consensus for the multi-agent networks subjected to cyber-attacks are given. Furthermore, the results are extended to the consensus issue of multiple subgroups with cyber-attacks. Numerical simulations are performed to demonstrate the effectiveness of the theoretical results.

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.

Layered event-triggered control for group consensus with both competition and cooperation interconnections

In this paper, the problem of group consensus of multi-agent systems that exchange information through two-layer directed communication network is investigated. Both competition and cooperation interconnections are considered, which is more in line with the reality. Based on layered event-triggered control strategy, agents only update control input and broadcast information to their neighborhood in discrete time instants according to the designed triggering conditions. Since the triggering conditions within two layers are different, the whole consensus process is asynchronous. We prove that the agents can achieve group consensus with the proposed control protocol and there is no Zeno behavior by choosing appropriate parameters.

Scaled Group Consensus in Multiagent Systems With First/Second-Order Continuous Dynamics.

We investigate scaled group consensus problems of multiagent systems with first/second-order linear continuous dynamics. For a complex network consisting of two subnetworks with different physical quantities or task distributions, it is concerned with this case that the agents' states in one subnetwork converge to a consistent value asymptotically, while the states in the other subnetwork approach another value with a ratio of the former. For the case of the information exchange being directed, novel consensus protocols are designed for both first-order and second-order dynamics to solve the scaled group consensus problems. By utilizing algebra theory, graph theory, and Lyapunov stability theory, several necessary and sufficient conditions are established to guarantee the agents' states reaching the scaled group consensus asymptotically. Finally, several simulation results are presented to demonstrate the effectiveness of the theoretical results.

Couple-group consensus for second-order multi-agent systems with the effect of second-order neighbours’ information

This paper investigates a couple-group consensus problem of second-order multi-agent systems with the impact of second-order neighbours’ information. For systems with/without time delays, couple-group consensus criteria are established in the form of linear matrix inequalities by utilizing both model transformation and stability theories. The main results indicate that the group consensus for multi-agent systems under the effect of second-order neighbours’ information can be achieved based on the premise of a generalized balanced couple. Finally, illustrative examples are presented to demonstrate the effectiveness of the theoretical results.

Reverse Group Consensus of Multi-Agent Systems in the Cooperation-Competition Network

In this paper, a reverse group consensus problem is investigated for the dynamic agents with the inputs in the cooperation-competition network which can be divided into two sub-networks. The weights between the agents in the same sub-network are positive, while the weights between the agents among different sub-networks are negative. Then, the reverse group consensus is firstly studied without the in-degree balance condition. By defining the mirror graph and establishing the solution of the multi-agent system, it is found that the reverse group consensus problem can be achieved if the mirror graph is strongly connected. The explicit expression of the error level is also derived, which would be vanished for multi-agent systems with some special kinds of inputs. Furthermore, as an extension, the decomposing of the cooperation-competition network is discussed, where the concept of the condensation undirected graph and the path balance condition are defined, and several effective sufficient conditions are obtained. Finally, numerical simulation demonstrates the effectiveness of the theoretical analysis.

Group consensus for second-order discrete-time multi-agent systems with time-varying delays under switching topologies

This paper addresses group consensus for multi-agent systems with switching topologies and time-varying delays, where all agents are described by discrete-time second-order dynamics. Based on the relationship between zero/nonzero in-degree graphs and nonnegative matrices group consensus criteria, which is presented in terms of easily checkable graph topology conditions, is obtained for multi-agent systems with time-varying delays under switching topologies. Furthermore, numerical examples are presented to illustrate the obtained results, and the essential of some conditions and assumptions is verified for given switching communication topologies.

Group consensus of multi-agent systems with communication delays

In this paper, we investigate group consensus problems for continuous-time multi-agent systems with time delays, where the agents׳ dynamics are controlled based on information from their neighbors at some discrete time instants. By utilizing nonnegative matrix theory and graph theory, the case with fixed topology and time-invariant delays is first considered, then the general case with switching topologies and time-varying delays is discussed. Some group consensus criteria are obtained in both cases, it is also shown that the agents in nonzero in-degree groups finally converge to the convex hull of those in zero in-degree groups. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.

Group Consensus for Multi-agent Systems Under the Effect of Coupling Strength Among Groups

This paper investigates a group consensus problem for multi-agent systems with fixed topologies. We focus on discussing the effect of the coupling strength among the agents in different groups, and obtain some conditions in form of linear matrix inequalities (LMIs) guaranteeing the group average consensus by using Lyapunov function methods. In order to study the effect of the coupling strength, we introduce two different parameters ã1, ã2 in the network topologies. Finally, illustrative examples are provided to demonstrate the effectiveness of the theoretical results with the two parameters.

Group consensus in multi-agent systems with switching topologies and time delays

In this paper, we investigate the group consensus problem for discrete-time multiagent systems with switching topologies and bounded time delays. The analysis in this paper is based on nonnegative matrix theory and graph theory. Under the assumption of common inter-group influence, the group consensus problem is proved to be solvable, if the union of the communication topology across any time interval with some given length contains group spanning trees. It is also shown that the nonzero in-degree groups finally converge to convex combination of the consensus states of the zero in-degree groups. The effectiveness of the theoretical results is finally demonstrated by the simulation example.

Second-order group consensus for multi-agent systems with time delays

This paper studies the group consensus problem of second-order multi-agent systems (MASs) with time delays. First, by state transformation method, the group consensus problem of multi-agent systems can be equivalently transformed into the asymptotical stability of a time-delay system. Then, by Lyapunov first method and Hopf bifurcation theory, respectively, we aim to find the upper bound of time delay τ⁎ such that the multi-agent systems can achieve group consensus for τ∈[0,τ⁎). Finally, simulation examples are given to show the effectiveness of our theoretical analysis.

Necessary and sufficient condition for the group consensus of multi-agent systems

This paper focuses on the group consensus issue of multi-agent systems, where the agents in a network can reach more than one consistent values asymptotically. A rotation matrix is introduced to an existing consensus algorithm for single-integrator dynamics. Based on algebraic matrix theories, graph theories and the properties of Kronecker product, some necessary and sufficient criteria for the group consensus are derived, where we show that both the eigenvalue distribution of the Laplacian matrix and the Euler angle of the rotation matrix play an important role in achieving group consensus. Simulated results are presented to demonstrate the theoretical results.