Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case

This article proposes an observer-based control strategy for networked multi-agent systems with constant communication delay and stochastic switching topology. First, using the system transformation method, the mean-square consensus problem of multi-agent systems can be converted into the mean-square stability problem of an equivalent system, and some equivalent conditions concerning the mean-square consensus are presented. Then, an example is given to illustrate that the connection weights should be regarded as the parameters to be designed, since they have a great effect on the mean-square consensus of multi-agent systems. By choosing appropriate connection weights, the mean-square consensus problem can be converted into the mean-square stabilisation problem of N-1 delay systems with stochastic switching signal, whose related observer-based stabilisability criteria can be established in the form of linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the multi-agent systems achieve mean-square consensus if and only if the union of graphs in the switching topology set has a directed spanning tree. Finally, numerical simulations are given to illustrate our results.     

Consensus of linear multi-agent systems with communication delays by using the information of second-order neighbours under intermittent communication topology

This paper investigates the consensus of identical linear multi-agent systems with aperiodic intermittent communication topology by using the information of second-order neighbours (two-hop neighbourhood). The protocols based on two-hop neighbourhood information and intermittent communication topology are designed, under which consensus is reached. If the communication rate is larger than the corresponding threshold value, the networks will accelerate consensus by using two-hop neighbourhood information. By means of switching systems theory and Lyapunov–Razumikhin theorem, consensus of multi-agent systems with communication delays and intermittent communication topology is reached by two-hop neighbourhood information. Finally, simulation examples are provided to show the effectiveness of the theoretical results.     

Consensus based overlapping decentralized estimation with missing observations and communication faults

In this paper a new algorithm for discrete-time overlapping decentralized state estimation of large scale systems is proposed in the form of a multi-agent network based on a combination of local estimators of Kalman filtering type and a dynamic consensus strategy, assuming intermittent observations and communication faults. Under general conditions concerning the agent resources and the network topology, conditions are derived for the convergence to zero of the estimation error mean and for the mean-square estimation error boundedness. A centralized strategy based on minimization of the steady-state mean-square estimation error is proposed for selection of the consensus gains; these gains can also be adjusted by local adaptation schemes. It is also demonstrated that there exists a connection between the network complexity and efficiency of denoising, i.e., of suppression of the measurement noise influence. Several numerical examples serve to illustrate characteristic properties of the proposed algorithm and to demonstrate its applicability to real problems.     

Stochastic consensus of double-integrator leader-following multi-agent systems with measurement noises and time delays

This paper studies a leader-following consensus problem of continuous-time double-integrator multi-agent systems with measurement noises and time-varying communication delays under directed topology. By utilising the neighbour position and velocity information, which are delayed and disturbed by measurement noises whose intensities are considered a function related to the neighbour position and velocity of agents, a distributed consensus protocol is presented, sufficient conditions of the tracking consensus in the sense of mean square are derived. Finally, the effectiveness of the proposed consensus protocol is proved by some simulations.     

Consensus control of second-order stochastic discrete-time multi-agent systems without velocity transmission

This article studies the almost-sure and the mean-square consensus control problems of second-order stochastic discretetime multi-agent systems with multiplicative noises. First, a control law based on the absolute velocity and relative position information is designed. Second, considering the existence of multiplicative noises and nonlinear terms with Lipschitz constants, the consensus control problem is solved through the use of a degenerated Lyapunov function. Then, for the linear second-order multi-agent systems, some explicit consensus conditions are provided. Finally, two sets of numerical simulations are performed.     

Periodic intermittent consensus of second-order agents networks with nonlinear dynamics

The consensus problem for a class of second-order agents networks via periodically intermittent control is investigated in this paper. A novel protocol is designed by periodic intermittent measurements and directed topology. Based on algebraic graph theory, matrix theory and Lyapunov control approach, some sententious conditions are obtained for reaching consensus in agents networks with fixed topology. Finally, one example is given to illustrate the effectiveness of the theoretical results.     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

Consensus control of multi-agent systems with missing data in actuators and Markovian communication failure

This article investigates the consensus problem of multi-agent systems (MASs) with imperfect communication both in channels and in actuators. The data transmission among agents may fail due to limited communication capacity, and the actuators may fail to receive information owing to noisy environment. We use a Markov chain approach to characterise the occurrence of the two types missing data in a unified framework. A sufficient consensus condition is first obtained in terms of linear matrix inequalities. Then, based on this condition, a novel controller design method is further developed such that the MAS with imperfect communication reaches mean-square consensus. It is shown that the consensus problem for MASs with switching topology can be regarded as a special case of the problem considered in this article, and the related theoretical results are presented as well. Numerical examples are provided to illustrate the effectiveness of the proposed approach.     

Distributed consensus of multi‐agent systems with general linear node dynamics and intermittent communications

Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi‐agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi‐agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low‐dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi‐step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi‐agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays

The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

具有随机丢包的网络化多自主体系统的一致性

研究具有随机丢包的网络化多自主体系统的均方一致性问题,其中不同自主体间的通信通道具有相同的丢包情况并且均服从马尔可夫(Markov)分布。首先,利用系统变换和迭代方法,得到了系统达到均方一致的一个初等充要条件。然后,利用矩阵理论和图论知识,如果拓扑图含有有向生成树,则可以将系统的均方一致性转化成一个线性Markov跳变系统的均方稳定性,并且可以建立线性矩阵不等式形式的均方可镇定准则。最后,通过相应的仿真实例说明了所得结论的可行性。     

Consensus for multi‐agent systems under double integrator dynamics with time‐varying communication delays

In this paper, the consensus control problems for multi‐agent systems under double integrator dynamics with time‐varying communication delays are investigated. We assume that the interaction graphs among agents are directed. Two kinds of protocols are considered. One is an absolute damping protocol, and the other is a relative damping protocol. For the first protocol, Lyapunov–Razumikhin functional techniques are used. We derive sufficient conditions that guarantee that all agents asymptotically reach consensus under fixed topology and switching topology, respectively. Moreover, the allowable upper bound for communication delays is given. For the second protocol, Lyapunov–Krasovskii functional techniques are used. Linear matrix inequality (LMI)‐form sufficient conditions are obtained to guarantee the consensus problems to be solved under fixed topology and switching topology, respectively. The allowable upper bound for communication delays is given as well. The feasibilities of the demanded LMIs are also discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Leader‐following control for multiple inertial agents

This paper investigates distributed controller design problem for a leader‐follower network in the presence of communication delays. Two main contributions are made in this work. First, the second‐order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second‐order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Consensus of second-order multi-agent systems with delayed nonlinear dynamics and aperiodically intermittent communications

In this paper, we investigate the consensus problem for second-order multi-agent systems with inherent delayed nonlinear dynamics and aperiodically intermittent communication. First, different from previous works, aperiodically intermittent communication is proposed. Moreover, two types of delay are considered. The first case is that the delay is small enough so that it is less than the minimum of communication width. The other one is that the delay is time-varying and large, and in this case, we do not restrict the delay less than the communication width. Different approaches are provided to study these two cases, and some conditions are obtained to achieve second-order consensus under a fixed strongly connected and balanced topology. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method.     

Consensus in multi‐agent systems with communication constraints

The problem of second‐order consensus is investigated in this paper for a class of multi‐agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second‐order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second‐order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Consensus of nonlinear multiagent systems with mode-dependent delay via stochastic sampled data under Markovian switching topologies

In this article, we investigate the mean-square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time-varying delay switch randomly which are regulated by a time-homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean-square consensus. For the undirected topology case, a low-dimensional LMI-based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.     

受外界干扰的离散多智能体系统的均方有界一致性

对有外界干扰的二阶离散多智能体系统,研究了在马尔可夫切换拓扑结构下的均方有界一致性问题.首先,设计了一个带有智能体位置和速度信息的控制协议.其次,在随机有界干扰的情况下,借助于矩阵分析方法以及Lyapunov函数,得到了闭环系统实现均方有界一致所需的代数条件,同时给出了各智能体状态误差的上界.最后,数值仿真验证了理论结果的有效性.     

积分事件触发策略下的线性多智能体系统领导跟随一致性

研究有向切换拓扑下线性多智能体系统的事件触发一致跟踪问题.大多数已有的工作研究了固定拓扑下的事件触发控制,然而,当智能体间联系随时间发生改变或通信拓扑随时间发生变化时,该控制策略失效.鉴于此,在考虑切换拓扑的基础上提出一种基于积分型事件触发的控制策略.首先,当拓扑图包含一棵生成树且领导者是根节点时,利用Lyapunov稳定性理论、代数图论和矩阵变换,基于积分型事件触发控制协议,在切换拓扑下多智能体系统达到领导跟随一致性;然后,当存在多个领导者时,基于设计的触发机制在切换拓扑下多智能体系统实现包含控制,上述两种情况下闭环系统均不存在Zeno现象;最后,通过仿真结果验证控制策略的有效性.     

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.     

Distributed consensus for multi-agent systems with delays and noises in transmission channels

This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols.