异质多智能体系统二分一致性的充要条件

针对由一阶智能体和二阶智能体组成的异质多智能体系统的二分一致性问题,对连续和离散系统情形分别设计了二分一致性协议。基于结构平衡的拓扑,通过规范变换实现了从具有敌对关系的系统到具有非负连接权重系统的转化,将二分一致性问题转变为一般一致性问题。进一步,运用代数图论和矩阵理论分析闭环控制系统的动态特性,得到了异质多智能体系统渐近实现二分一致性的充要条件。最后通过数值模拟验证了所得结果的有效性。     

符号网络下一类非线性二分一致性系统的跟踪控制

研究具有对抗交互的一类非线性多智能体系统的二分一致性跟踪控制问题,借助有向符号图刻画智能体之间的通信关系,并假定符号图是结构平衡的.进一步,借助符号图网络对二分一致性跟踪问题进行公式化描述.基于最近邻原则,结合拉普拉斯矩阵、牵制矩阵、符号函数、耦合增益参数等,设计分布式控制律.利用Barbalat引理和李亚谱诺夫函数证明整个闭环系统的渐近稳定性,在保持闭环系统稳定的条件下推导出耦合增益的下界.最后通过仿真验证所提出方法的有效性.     

Bipartite Byzantine-resilient event-triggered consensus control of heterogeneous multi-agent systems

This article studies the bipartite resilient event-triggered consensus control for a class of the heterogeneous multi-agent systems. Due to the external cyberattacks, some agents may become the Byzantine agents and will affect the behavior of the other agents. To improve the security of the multi-agent systems against the Byzantine agents, a novel bipartite event-triggered heterogeneous mean-subsequence-reduced algorithm is designed. First, to handle the heterogeneous multi-agent systems, a state transformation is carefully designed, to facilitate the design and analysis of the bipartite resilient consensus algorithm. Based upon the designed state transformation, the bipartite resilient control inputs are constructed, where the structural balance analysis shows that the resulting effective signed graph and the equivalent signed graph are both structurally balanced, if the signed graph of the multi-agent systems is structurally balanced. In addition, a dynamic event-triggered mechanism is proposed, where a set of dynamic factors are introduced into the event-triggered functions to prevent the usage of the global topology information. By virtue of the designed algorithm, it is guaranteed that the heterogeneous multi-agent systems can achieve the bipartite consensus in the presence of the Byzantine agents, and the communication burden among the agents can be reduced. The numerical simulations are conducted to verify the effectiveness of the proposed algorithm.     

Bipartite tracking of homogeneous and heterogeneous linear multi-agent systems

In this paper, we consider bipartite tracking of linear multi-agent systems with a leader. Both homogeneous and heterogeneous systems are investigated. The communication between agents is modelled by a directed signed graph, where the negative (positive) edges represent the antagonistic (cooperative) interactions among agents. Linear Quadratic Regulator (LQR)-based approach is used to derive the distributed protocol for the follower agent to achieve bipartite tracking of the leader. It is shown that solving the bipartite tracking problem over the structurally balanced signed graph is equivalent to solving the cooperative tracking problem over a corresponding graph with nonnegative edge weights. This bridges the gap between the newly raised bipartite tracking problem and the well-studied cooperative tracking problem. Three novel control protocols are proposed for both cooperative and bipartite output tracking of heterogeneous linear multi-agent systems. Numerical examples are given to show the effectiveness of our control protocols.     

Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks

In this paper, a bipartite consensus problem is considered for a high‐order multiagent system with cooperative‐competitive interactions and unknown time‐varying disturbances. A signed graph is used to describe the interaction network associated with the multiagent system. The unknown disturbances are expressed by linearly parameterized models, and distributed adaptive laws are designed to estimate the unknown parameters in the models. For the case that there is no exogenous reference system, a fully distributed adaptive control law is proposed to ensure that all the agents reach a bipartite consensus. For the other case that there exists an exogenous reference system, another fully distributed adaptive control law is also developed to ensure that all the agents achieve bipartite consensus on the state of the exogenous system. The stability of the closed‐loop multiagent systems with the 2 proposed adaptive control laws are analyzed under an assumption that the interaction network is structurally balanced. Moreover, the convergence of the parameter estimation errors is guaranteed with a persistent excitation condition. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed adaptive bipartite consensus control laws for the concerned multiagent system.     

通信受限的多智能体系统二分实用一致性

针对存在量化数据、通信时滞等通信约束以及带有竞争关系的多智能体系统, 研究其二分实用一致性问题, 提出了一种基于量化器的分布式控制协议. 该协议基于结构平衡拓扑假设, 通过规范变换将具有竞争关系系统转变为具有非负连接权重系统, 使二分实用一致性问题转变为一般实用一致性问题. 利用微分包含理论、菲利波夫解的框架、代数图论以及Lyapunov稳定性理论, 证明了在本文所提控制策略下, 具有竞争关系的多智能体系统能实现二分实用一致, 即智能体状态收敛至模相同但符号不同的可控区间, 并给出了误差收敛上界值. 仿真试验进一步验证了理论结果的有效性.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

Group consensus of multi-agent systems in directed networks with noises and time delays

In this paper, group consensus problems in fixed directed networks of dynamic agents are investigated. Group consensus means that the agents in each group share a consistent value while there is no agreement between any two groups. Based on algebraic graph theory, sufficient conditions guaranteeing group consensus under the proposed control protocol in the presence of random noises and communication delays are derived. The analysis uses a stability result of Mao for stochastic differential delay equations, which ensures the consensus can be achieved almost surely and exponentially fast. Numerical examples are provided to demonstrate the availability of the obtained results as well as the effect of time delay/noise intensity.     

Semi‐global bipartite output consensus of heterogeneous multi‐agent systems subject to input saturation by finite‐time observer

In this paper, the semi‐global bipartite output consensus problem of heterogeneous linear multi‐agent systems is studied. Compared with related works, both cooperative interactions and antagonistic interactions between agents are considered, and the input saturation on each follower is taken into account. First, two distributed finite‐time observers are designed to recover the leader's state. Particularly, the setting time can be independent of any initial states. Due to the antagonistic interactions, estimation values are the same as the leader's state in modulus but may not in sign. Then, the low‐gain feedback technique is used to develop the distributed control law for each follower. Moreover, we summarize a framework for solving the semi‐global bipartite output consensus problem of heterogeneous multi‐agent systems subject to input saturation. Finally, examples are given to illustrate the results.     

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.     

Bipartite output consensus in networked multi-agent systems of high-order power integrators with signed digraph and input noises

In this paper, we concentrate on investigating bipartite output consensus in networked multi-agent systems of high-order power integrators. Systems with power integrator are ubiquitous among weakly coupled, unstable and underactuated mechanical systems. In the presence of input noises, an adaptive disturbance compensator and a technique of adding power integrator are introduced to the complex nonlinear multi-agent systems to reduce the deterioration of system performance. Additionally, due to the existence of negative communication weights among agents, whether bipartite output consensus of high-order power integrators can be achieved remains unknown. Therefore, it is of great importance to study this issue. The underlying idea of designing the distributed controller is to combine the output information of each agent itself and its neighbours, the state feedback within its internal system and input adaptive noise compensator all together. When the signed digraph is structurally balanced, bipartite output consensus can be reached. Finally, numerical simulations are provided to verify the validity of the developed criteria.     

Modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions

This paper addresses the modulus consensus in a network of singularly perturbed systems, all of which own multi-time scales characteristics. The interactions among the agents are collaborative and antagonistic interactions, and it can been modelled by a signed directed graph. Also, the effect of time-varying delay has been taken into account when modelling the agent dynamics. Based on singularly perturbed decomposition method, Kronecker product technique and the comparison principle, several sufficient conditions are presented under which networked singularly perturbed time-varying delay systems with collaborative and antagonistic interactions achieve modulus consensus. Moreover, the upper bound of singular perturbation parameter is deduced explicitly. Two simulation examples are presented to illustrate the validity of the proposed results.     

含时延约束的多智能体系统二分一致性

针对多智能体系统中信息交互存在通信时延这一约束,在无向符号图拓扑结构下分别研究了含固定时延和时变时延的一阶多智能体系统二分一致性问题。通过设计相应的控制协议,使得该系统收敛到两个模值相同但符号不同的状态。在稳定性分析中,利用广义Nyquist准则的方法,得到含固定时延多智能体系统实现二分一致性的充分条件;对含时变时延系统构造包含三重积分项的Lyapunov函数,利用积分不等式和线性矩阵不等式理论,并结合自由矩阵的方法得到含时变时延多智能体系统实现二分一致性的充分条件。最后,数值仿真验证了所得结论的有效性和正确性。     

Regional consensus of linear differential inclusions subject to input saturation

In this article, we consider regional consensus problem for a group of identical linear systems represented by a linear differential inclusion over an undirected communication topology. Each vertex system of the linear differential inclusion is represented by a general linear system subject to input saturation, and hence only regional consensus can be achieved. For given saturated distributed linear control protocols, we establish a set of conditions under which these control protocols achieve regional consensus and a level set of a Laplacian quadratic function can be used as an estimate of the domain of consensus. These conditions are given in the form of matrix inequalities and involve the properties of the communication topology. Based on these matrix inequalities, we formulate a linear matrix inequalities based optimization problem for obtaining as large an estimate of the domain of consensus as possible. By viewing the gain matrix in the consensus algorithms as an additional variable, this optimization problem can be adapted for the design of the consensus protocols. Simulation results illustrate the effectiveness of our proposed approach.     

Optimal strategies in the average consensus problem

Let a set of communicating agents compute the average of their initial positions, where every agent is restricted to communicate to a given small number of other agents (average consensus problem). We prove that the optimal topology of communication is given by a de Bruijn graph. Consensus is then reached in finitely many steps. This solution is valid when the number of agents is an exact power of the out-degree of the communication graph. We introduce an algebraic tool, the shifted Kronecker product, and a more general family of strategies, also based on a de Bruijn communication graph. Those strategies are compared to Cayley strategies in terms of the speed of convergence. We also show that quantized communication between the agents still allows finite convergence, to a consensus, which is not in general the average of the initial positions.     

对抗网络下时滞非线性多智能体系统固定时间二分一致性

本文针对一类存在输入时延的非线性多智能体系统,研究了其在结构平衡的无向符号图下的固定时间二分一致性问题.首先,本文针对智能体间相互合作与相互竞争的关系,设计了一类存在输入时延的多智能体系统固定时间分布式一致性控制协议,使得系统状态在固定时间内收敛到数值相同但符号相反的两个值,且收敛时间上界与初始状态无关.随后,利用Lyapunov稳定性理论和代数图论给出了在存在输入时延的情况下多智能体系统实现固定时间二分一致性的充分条件和收敛时间的上界值,证明了控制算法的稳定性.最后,仿真实例验证了所提固定时间二分一致性算法和理论结果的有效性.     

Network-to-network bipartite consensus under event-triggered control over heterogeneous topologies

This article investigates the event-triggered control scheme for network-to-network consensus problem over heterogeneous topologies. The cooperative-competitive interactions among agents are considered. A distributed event-triggered control mechanism for the multi-agent system is proposed without requiring continuous inter-neighboring communications. Time-dependent triggering conditions are presented. By using Lyapunov stability theory, the matrix, and the algebraic graph theory, bipartite consensus is proved, and Zeno behavior is excluded. Finally, simulations are provided to prove the effectiveness of the obtained results.     

切换拓扑下多自主体系统的事件触发一致性控制

本文针对一阶非线性多自主体系统,考察了切换拓扑下的事件触发一致性控制问题.当切换拓扑子图的并图包含有向生成树时,基于一阶保持器提出了一种分布式事件触发一致性算法,用以降低网络的通信负载.运用迭代法和不等式法,得到了多自主体系统达到有界一致性的充分条件.此外,证明了所提事件触发机制不存在Zeno现象,并得到了触发间隔的正下界.最后,给出仿真实例,验证了所提事件触发一致性算法和理论分析结果的有效性.     

Robust and nonfragile consensus of positive multiagent systems via observer‐based output‐feedback protocols

This article investigates the consensus problem for positive multiagent systems via an observer‐based dynamic output‐feedback protocol. The dynamics of the agents are modeled by linear positive systems and the communication topology of the agents is expressed by an undirected connected graph. For the consensus problem, the nominal case is studied under the semidefinite programming framework while the robust and nonfragile cases are investigated under the linear programming framework. It is required that the distributed state‐feedback controller and observer gains should be structured to preserve the positivity of multiagent systems. Necessary and/or sufficient conditions for the analysis of consensus are obtained by using positive systems theory and graph theory. For the nominal case, necessary and sufficient conditions for the codesign of state‐feedback controller and observer of consensus are derived in terms of matrix inequalities. Sufficient conditions for the robust and nonfragile consensus designs are derived and the codesign of state‐feedback controller and observer can be obtained in terms of solving a set of linear programs. Numerical simulations are provided to show the effectiveness and applicability of the theoretical results and algorithms.     

Robust iterative learning protocols for finite-time consensus of multi-agent systems with interval uncertain topologies

This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results.