Couple-group Consensus Research Articles

Couple-group consensus of heterogeneous nonlinear multi-agent systems with cooperative–competitive interactions and input saturation

Couple-group consensus of multi-agent systems with cooperative–competitive interactions and input saturation is studied under fixed and switching topologies based on pinning control and event-triggered control. First, for heterogeneous multi-agent systems consisting of first- and second-order agents, we propose two new distributed event-triggered control protocols, and the control protocols both enable the groups of agents to achieve the desired consensus state, which can effectively reduce the number of controller updates and save communication resources. Second, based on the Lyapunov stability theory, the sufficient conditions are established for the couple-group consensus of multi-agent systems. Meanwhile, Zeno behavior is excluded. Third, the effectiveness and feasibility of the control methods proposed in this paper are verified via some simulation examples.

The Couple-Group Consensus of Heterogeneous Multi-Agent Systems with Different Leaders Under Markov Switching in Cooperative-Competitive Networks

The Couple-Group Consensus of Heterogeneous Multi-Agent Systems with Different Leaders Under Markov Switching in Cooperative-Competitive Networks

Couple-Group Consensus of Heterogeneous Multi-Agents Systems With Markov Switching and Cooperative-Competitive Interaction

In this paper, couple-group consensus is investigated for a kind of heterogeneous multi-agent systems (HMASs) with Markov switching. Some novel couple-group consensuses have been proposed, in which cooperative-competitive interaction, Markov switching and time delay are all considered. For Markov switching, the transitive rate of probability can be divided into two cases: known or partly known. Based on stochastic delta operator, probability, graph and stability theories, the leader-following and pinning couple-group consensus of this system be converted into analyzing the stability of related switching delta operator system. In the obtained results, some conservative conditions, such as the balance of in or out degree, strong connectivity and containing a spanning tree, can be longer strictly demanded. Some numerical examples are given to show the validity of the acquired results.

Networked-prediction-based group output consensus and stability with reference input and communication constraints

The issue of stability and group output consensus is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints(e.g., time delays and data loss) in this paper. Firstly, the couple-group output consensus is analyzed theoretically, the communication constraints are compensated by the prediction method. Secondly, the necessary and sufficient condition is given to ensure the stability of the system, achieve the couple-group consensus with reference input control, and relax the topology constraint of in-degrees balance by cooperative-competitive interactions. Furthermore, the result of couple-group consensus is extended to multi-group consensus based on a novel predictive control algorithm. Finally, a numerical simulation shows that the proposed networked predictive control method can effectively overcome the communication constraints, the dynamic performance and control effect are similar to the traditional control without communication constraints.

Couple-Group Consensus for First Order Discrete-Time Multiagent Systems With Competition-Cooperation and Input Saturation Constraints

Collaborative consensus control of multiagent systems has become an important research topic in the field of artificial intelligence in recent years. This paper deals with the couple-group consensus for the first order discrete-time systems with input saturation constraints. Compared to most previous studies, this article focuses on the control input constraints phenomenon in couple-group consensus problem. Based on the relationship between competition and cooperation, a new negotiation protocol is designed to achieve couple-group consensus. Furthermore, combining graph theory with Lyapunov theorem, the control gain condition is obtained. Finally, the results of numeric modeling show that the method is correctness and effectiveness.

Couple-group consensus for heterogeneous MASs under switched topologies in cooperative-competitive systems: A hybrid pinning and delta operator skills

In this paper, pinning control and delta operator skills are applied to study couple-group consensus for heterogeneous MASs (multi-agent systems) with switched topology in cooperative-competitive networks. A new couple-group consensus agreement has been designed for this heterogeneous MASs with time delay. On the basis of delta operator and stability theory, couple-group consensus of the continuous or discrete systems can be transformed to analyze stability of a system with time lag. By using stability theory and LMI (Linear matrix inequality) technique, some meaningful results are put forward to obtain couple-group consensus of the heterogeneous MASs. In addition, these conclusions are also suitable for MASs whose switched topologies networks can’t meet the equilibrium of in-degree or can’t meet the requirements of any sub-topology with a spanning tree. In the end, some digital experiments are listed to prove the validity of the obtained achievements.

Couple-Group Consensus of Cooperative-Competitive Heterogeneous Multiagent Systems: A Fully Distributed Event-Triggered and Pinning Control Method.

This article discusses the couple-group consensus for heterogeneous multiagent systems via event-triggered and pinning control methods. Considering cooperative-competitive interaction among the agents, a novel group consensus protocol is designed. As inducing the time-correlation threshold function, a class of fully distributed event-triggered conditions without depending on any global information is proposed. Utilizing the Lyapunov stability theory, some sufficient conditions are obtained. Under hybrid event triggered and pinning control, pinning control strategies are first introduced. It is shown that under the proposed strategies, all agents can asymptotically achieve pinning couple-group consensus with discontinuous communication in a fully distributed way. Furthermore, the Zeno behavior for each agent is overcome. Finally, the reduction of the systems' controller update frequency and the correctness of our conclusions are illustrated by some simulations.

The Weighted Couple-Group Consensus for a Kind of Continuous Heterogeneous Multi-Agent Systems Based on Self-Adaptive and Cooperative-Competitive Mechanism

In this paper, the weighted couple-group consensus is investigated for a kind of continuous heterogeneous multi-agent systems in the cooperation-competition networks with time-delay. A novel weighted couple-group consensus protocol is proposed on basis of self-adaptive and cooperative-competitive mechanism. In this novel couple-group control protocol, self-adaptive regulation, weighted-distribution, cooperation-competition, position and velocity are considered. By applying the graph theory, complex frequency analysis method and linear algebra theory, some sufficient conditions have been given to guard the success of the couple-group consensus for this kind of heterogeneous multi-agent systems. Furthermore, the upper limit of the time delay may be computed if the weighted parameters are determined. The results show that the multi-agent system can converge to couple-group consensus state only if the upper bound input time-delay is satisfied the given time span. Some simulation examples show the validity of the obtained results.

Couple-Group Consensus for Cooperative-Competitive Heterogeneous Multiagent Systems: Hybrid Adaptive and Pinning Methods

In this article, the problem of couple-group consensus for the heterogeneous multiagent systems (MASs) composed of first-order and second-order agents are investigated by hybrid pinning and adaptive control methods, respectively. A novel distributed control protocol of group consensus is proposed via the cooperative-competitive relationship between the agents. Based on algebraic graph theory, matrix analysis and Lyapunov stability theorem, the sufficient conditions and corresponding pinning strategies for the heterogeneous MASs with the weakly connected topology are obtained. In addition, we find that the value of pinning gain should meet a certain condition for guaranteeing the achievement of group consensus. Finally, the validity of our results is verified by some simulated examples.

Couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies**Project supported by the National Natural Science Foundation of China (Grant Nos. 61503002 and 61573008).

The paper addresses the issue of couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control. Both fixed and Markovian switching communication topologies are considered. By employing linear transformations, the closed-loop systems are converted into reduced-order systems and the couple-group consensus issue under consideration is changed into a stochastic control problem. New conditions for the mean-square asymptotic stability and performance of the reduced-order systems are proposed. On the basis of these conditions, constructive approaches for the design of the output-feedback control protocols are developed for the fixed communication topology and the Markovian switching communication topologies, respectively. Finally, two numerical examples are given to illustrate the applicability of the present design approaches.

Couple-Group Consensus: A Class of Delayed Heterogeneous Multiagent Systems in Competitive Networks

This paper discusses the couple-group consensus issues of a class of heterogeneous multiagent systems containing first-order and second-order dynamic agents under the influence of both input and communication delays. In distinction to the existing works, a novel distributed coordination control protocol is proposed which is not only on the foundation of the competitive interaction between the agents but also has no virtual velocity estimation in the first-order dynamics. Furthermore, without the restrictive assumptions existing commonly in the related works, several sufficient algebraic criteria are established for the heterogeneous systems to realize couple-group consensus asymptotically. The obtained conclusions show that the achievement of the systems’ couple-group consensus intimately relates to the coupling weights between the agents, the systems control parameters, and the input time delays of the agents, while communication time delays between the agents are irrelevant to it. Finally, several simulations are illustrated to verify the effectiveness of the obtained theoretical results.

Couple-Group Consensus for Multiagent Systems via Time-Dependent Event-Triggered Control

This paper investigates couple-group consensus problems for multiagent first-order and second-order systems. Several consensus protocols are proposed based on the time-dependent distributed event-triggered control. For the case of no communication delays, the time-dependent event-triggered strategies are applied to couple-group consensus problems. Based on the matrix theory, algebraic conditions for couple-group consensus are established. For the system with communication delays, based on event-triggered strategies, a Lyapunov-Krasovskii functional is constructed to prove the input-to-state stability of the systems. Moreover, Zeno behavior is excluded. Finally, numeral examples are given to illustrate the effectiveness of these results.

Couple-group consensus for discrete-time heterogeneous multiagent systems with cooperative–competitive interactions and time delays

Abstract We investigate couple-group consensus problems for a class of discrete-time heterogeneous systems consisting of first-order and second-order agents under the influence of communication and input time delays. A novel consensus protocol is designed by utilizing cooperative and competitive interactions among agents, so that we solve the couple-group consensus problems casting off a conservation condition of in-degree balance which widely exists in relevant articles. Based on frequency-domain analysis and matrix theory, some sufficient conditions are derived to ensure the achievement of group consensus in some cases, and the upper bound of input time delays are consequently estimated. The results show that the achievement of couple-group consensus is closely relate to the coupling weights between the agents, the control parameters of the systems, the sampled information of discrete-time systems as well as the agents’ input time delays, while it is irrelevant to communication delays. Finally, we provide several simulations to illustrate the correctness of the theoretical results.

Couple-group consensus conditions for general first-order multiagent systems with communication delays

In this paper, we establish group consensus conditions for first-order systems with communication delays using the relationship between time-delay parameter and the closed-loop characteristic roots. At first, we derive necessary conditions for the delay-free case, then we proceed to the delay-induced case. Contrary to most studies on group consensus where the conditions are derived considering the Laplacian of the entire multiagent network, we derive the group consensus conditions based on the Laplacian matrices that describe each subgroup and the inter-connection among sub-groups. Simulation studies are used to validate the derived conditions.

Event-triggered tracking control for couple-group multi-agent systems

This paper mainly investigates the event-triggered tracking control for couple-group multi-agent systems in a disturbance environment, where the topology of the agents is switching. Consensus protocol is designed for the case that some agents reach a consistent value, while the other agents reach another consistent value. Then, event-triggered control laws are designed to reduce the frequency of individual actuation updating for discrete-time agent dynamics. Moreover, by applying the Lyapunov function method, a sufficient condition of couple-group consensus is established in terms of a matrix inequality when the communication topology is switching. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.

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.

Heterogeneous and Competitive Multiagent Networks: Couple-Group Consensus with Communication or Input Time Delays

This paper discusses the couple-group consensus problems for a class of heterogeneous multiagent networks including the following two cases: with communication and input time delays, respectively. Different from the related cooperative networks, two novel delayed group consensus protocols are designed based on the competitive relationship between the agents. Furthermore, we absolutely relax the in-degree balance and other restrictive preconditions which existed in the relevant works. Some sufficient algebraic criteria for the achievement of couple-group consensus and the upper bound of the input time delays are technically obtained via the frequency domain method and matrix theory, respectively. The results show that the achievement of the couple-group consensus depends on the second-order agents’ in-degree and the control parameters of the systems, whereas it is independent of the communication time delays. Meanwhile, the upper bound of the input time delay is determined by the control parameters and the in-degree of the first-order agents. Finally, the validity of the proposed results is verified by several simulated examples.

On Couple-Group Consensus of Multiagent Networks with Communication and Input Time Delays

This paper investigated the couple-group consensus problems of the multiagent networks with the influence of communication and input time delays. Based on the frequency-domain theory, some algebraic criteria are addressed analytically. From the results, it is found that the input time delays and the coupling strengths between agents of the systems play a crucial role in reaching group consensus. The convergence of the system is independent of the communication delays, but it will affect the convergence rate of the system. Finally, several simulated examples are provided to verify the validity and correctness of our theoretical results.

Couple-group consensus of continuous-time multi-agent systems under Markovian switching topologies

This paper studies the couple-group consensus problem of multi-agent systems with general linear time-invariant dynamics. The interaction among agents is governed by a continuous-time homogeneous Markov process, whose state space corresponds to all the possible communication topologies. A linear consensus protocol is introduced to realize the couple-group consensus, where the agents in one subnetwork reach a consistent state while those in the other subnetwork reach another consistent state. When the agent dynamics is stabilizable, it is found that the couple-group consensus can be achieved under some mild algebraic and topological conditions of the inter-communication and intra-communication of agents in the two subnetworks. Appropriate consensus gain is designed and the speed to consensus is derived. Finally, three numerical examples are included to illustrate the obtained results.

Group consensus for multiple networked Euler-Lagrange systems with parametric uncertainties

In this paper, a group consensus problem is investigated for multiple networked agents with parametric uncertainties where all the agents are governed by the Euler-Lagrange system with uncertain parameters. In the group consensus problem, the agents asymptotically reach several different states rather than one consistent state. A novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed for each agent in order to solve the couple-group consensus problem. It is shown that the group consensus is reachable even when the system contains the uncertain parameters. Furthermore, the multi-group consensus is discussed as an extension of the couple-group consensus, and then the group consensus with switching topology is considered. Simulation results are finally provided to validate the effectiveness of the theoretical analysis.