On average consensus in directed networks of agents with switching topology and time delay

In this article, the average consensus problem in directed networks of agents with both switching topology and coupling delay is investigated. First, based on a specific orthogonal transformation of the Laplacian matrix, an important proposition for verifying the positive definiteness of a class of quadratic forms is provided, which is of independent interest in matrix theory. And the relation between weakly connected and strongly connected digraphs is also investigated. Then, it is proved that all the agents reach the average consensus asymptotically for appropriate time delay if the communication topology keeps weakly connected and balanced. Finally, a numerical example is given to demonstrate the effectiveness and advantage of the new result.     

Leader-following consensus of stochastic dynamical multi-agent systems with fixed and switching topologies under proportional-integral protocols

With the rapid development of swarm intelligence, consensus problem for multi-agent systems (MASs) has attracted substantial attention. To deal with the leader-following consensus problems in stochastic dynamical MASs with fixed and switching topologies, this article designed proportional-integral (PI) control protocols. On the basis of algebraic graph theory and stochastic analysis techniques, by selecting appropriate Lyapunov functions, it is theoretically shown that leader-following consensus of MASs with stochastic dynamics underlying fixed and switching topologies can be achieved in mean square, respectively. Sufficient criteria are derived for selecting the PI control gains. Finally, the theoretical results are illustrated through several numerical simulations.     

Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies

This article studies a consensus problem for a group of high-order dynamic agents with fixed and switching topologies. Two linear consensus protocols, which only depend on the agent's own information and its neighbours' partial information, are proposed, respectively, for the group with and without communication time-delays. For the case of fixed topology and zero communication time-delay, a necessary and sufficient condition for the consensus is established. The parameter design of the protocol is also discussed. Under switching topology, the consensus is investigated for two cases: the case of zero communication time-delay and the case of nonuniform communication time-delays. For each case, a sufficient condition for the consensus is provided. Moreover, for a group of double/triple-integrator agents with fixed topology and uniform constant time-delay, some necessary and sufficient conditions for the consensus are given. Finally, numerical simulations are worked out to illustrate the effectiveness of the theoretical results.     

Cluster consensus of high-order multi-agent systems with switching topologies

This paper investigates the cluster consensus problems of generic linear multi-agent systems with switching topologies. Sufficient criteria for cluster consensus, which generalise the results in existing literatures, are derived for both state feedback and observer-based control schemes. By using an averaging method, it is shown that cluster consensus can be achieved when the union of the acyclic topologies contains a directed spanning tree within each cluster frequently enough. We also provide a principle to construct digraphs with inter-cluster cyclic couplings that promote cluster consensus regardless of the magnitude of inter-agent coupling weights. Finally, numerical examples are given to demonstrate the effectiveness of the proposed approaches.     

Distributed consensus filter on directed switching graphs

We consider distributed estimation on a directed graph with switching topologies. Motivated by a recent PI consensus filter, we modify the protocol and remove the requirement of bidirectional exchange of neighboring gains for fixed topologies. We then extend the protocol to switching topologies and propose a new hybrid consensus filter design. Convergence results under both balanced directed, and general directed graphs are given for switching graphs. Consensus error bounds are analytically derived in the case of time‐varying inputs. Satisfactory simulation results are shown. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus of output-coupled high-order linear multi-agent systems under deterministic and Markovian switching networks

Consensus problem for high-order multi-agent systems is considered under deterministic and Markovian switching topologies. Only relative output information of agents is assumed to be available through the networks. First, a necessary and sufficient condition for achieving a consensus under a fixed communication network is presented. Based on this result and the stability of switched systems, a high-order multi-agent system with the proposed low-gain controller is shown to reach a consensus under deterministic switching network if the total time when the network is disconnected is, in some senses, smaller than the total time of the network being connected. Furthermore, the conditions sufficient for a high-order multi-agent system to reach an almost sure and mean-square consensus, under Markovian switching networks, are presented. Finally, illustrative examples are given to demonstrate the results.     

Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies

In this article, we study distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. The analysis is based on graph theory and nonnegative matrix theory. We propose two kinds of consensus protocols based on the consensus protocol of first-order and second-order multi-agent systems. Some necessary and sufficient conditions that the heterogeneous multi-agent system solves the consensus problems under different consensus protocols are presented with fixed topology. We also give some sufficient conditions for consensus of the heterogeneous multi-agent system with switching topology. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical 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.     

高阶有向积分器网络的包含控制

研究高阶固定有向积分器网络的包含控制问题。针对静止和运动的领导者,分别为跟随者提出了不同的控制协议。领导者是静止的情况下,应用拉普拉斯变换终值定理提出线性控制协议,驱使跟随者渐近进入由多个领导者所构成的静态凸包中;领导者是移动的情况下,提出非线性控制协议,以保证跟随者能够渐近进入由多个领导者所构成的动态凸包中,并使跟随者一直保持在该凸包中,同时提出了能够达到这一目标的充分条件。仿真结果验证了该理论分析的正确性。     

Guaranteed performance consensus problems for nonlinear multi-agent systems with directed topologies

The guaranteed performance consensus problem for multi-agent systems with Lipschitz nonlinear dynamics is investigated, where the interaction topology is directed. Both switching and fixed interaction topologies are considered. By the matrix transformation method, the guaranteed performance consensus problems are transferred into guaranteed performance stabilisation problems. Then, the criteria of guaranteed performance consensus for nonlinear multi-agent systems with switching and fixed interaction topologies are obtained, respectively. For the introduced performance function, an upper bound is given. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed results.     

Sampled-data consensus of general linear multi-agent systems under switching topologies: averaging method

This paper investigates sampled-data consensus problems of general linear multi-agent systems under switching topologies. To perform the consensus analysis by the averaging method, the multi-agent system in the sampled-data setting is first converted into the continuous-time system with the input delay. Then, the approximate relationship between the states of this input delay system and the states of its averaged system is established by using the tool from non-standard analysis. Subsequently, a sufficient condition ensuring the sampled-data consensus is obtained by linear matrix inequalities. It is shown that the sampled-data consensus of general linear multi-agent systems, including exponential unstable agents, can be achieved, if the speed of topology switching is fast enough and the sampled-data consensus under the averaging topology can be achieved. Finally, numerical simulations are provided to demonstrate the effectiveness of theoretical analyses.     

Passivity-based consensus for linear multi-agent systems under switching topologies

This paper studies the passivity-based consensus analysis and synthesis problems for a class of stochastic multi-agent systems with switching topologies. Based on Lyapunov methods, stochastic theory, and graph theory, new different storage Lyapunov functions are proposed to derive sufficient conditions on mean-square exponential consensus and stochastic passivity for multi-agent systems under two different switching cases, respectively. By designing passive time-varying consensus protocols, the solvability conditions for the passivity-based consensus protocol synthesis problem, i.e., passification, are derived based on linearization techniques. Numerical simulations are provided to illustrate the effectiveness of the proposed methods.     

Reaching global leaderless consensus in directed networks via smooth and bounded control

This short communication revisits the leaderless consensus problem in directed networks. The network topology is described by a general directed graph which is only needed to contain at least a directed spanning tree, and is not necessarily strongly connected. A bounded and smooth control law using the hyperbolic tangent function is developed as the consensus protocol. Explicit stability analysis based on Lyapunov's second method and the concept of condensation graph is given. The proposed approach transforms the leaderless consensus problem into two subproblems: reaching leader-following consensus under a graph containing a directed spanning tree with the leader being the root node and reaching leaderless consensus under a strongly connected graph. Remarkably, a perturbed system is formulated as the bridge between these two subproblems which are solved by Lyapunov's second method. The global leaderless consensus is achieved based on the stability of the perturbed system. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed approach.     

Transcale average consensus of directed multi-vehicle networks with fixed and switching topologies

This paper contributes to solving a class of so-called ‘transcale average consensus’ problems for directed networks of vehicles with single-integrator dynamics. It generalises the idea of average consensus by taking into account the measurement scale of every vehicle's information state. Using the nearest neighbour-interaction rules, distributed algorithms are presented which are shown with the ability to achieve the transcale average consensus for directed networks associated with balanced graphs. Such consensus results are applicable to networks in the presence of both fixed topology and switching topologies, which are also illustrated via simulation tests. Moreover, improved algorithms and results of consensus are given for directed networks associated with unbalanced graphs.     

Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays

In this article, we consider average consensus problem in directed delayed networked multi-agent systems having impulsive effects with fixed topology and stochastic switching topology. A simple impulsive consensus protocol for such networks is proposed, and some generic criteria for solving the average consensus problem are analytically derived. It is shown that a directed delayed networked multi-agent system can achieve average consensus globally exponentially with suitable impulsive gain and impulsive interval. Subsequently, two typical illustrative examples, along with computer simulation results, are provided to visualise the effectiveness and feasibility of our theoretical results.     

Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology

This paper is concerned with the fixed-time consensus problem of multi-agent systems. Unlike conventional consensus-based investigations, where nonlinear inherent dynamics satisfying the Lipschitz continuous condition is assumed or simply no inherent dynamics is involved for each agent, we are dealing with a more general case: agents with discontinuous nonlinear inherent dynamics. By using non-smooth analysis and fixed-time stability techniques, distributed protocols are proposed to achieve the fixed-time consensus over fixed and switching topology. Then, for a class of linear multi-agent systems, a new distributed controller is proposed to further reduce the calculation cost while achieving the agreement. A distinctive feature of the work is that the estimation of settling time for consensus is independent of initial states of agents, which provides flexibility for applications implemented in unknown environment. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.     

Graph-balancing algorithms for average consensus over directed networks

Consensus strategies find extensive applications in coordination of robot groups and decision-making of agents. Since balanced graph plays an important role in the average consensus problem and many other coordination problems for directed communication networks, this work explores the conditions and algorithms for the digraph balancing problem. Based on the analysis of graph cycles, we prove that a digraph can be balanced if and only if the null space of its incidence matrix contains positive vectors. Then, based on this result and the corresponding analysis, two weight balance algorithms have been proposed, and the conditions for obtaining a unique balanced solution and a set of analytical results on weight balance problems have been introduced. Then, we point out the relationship between the weight balance problem and the features of the corresponding underlying Markov chain. Finally, two numerical examples are presented to verify the proposed algorithms.     

基于有向通信拓扑的高阶分布式一致性算法

为了提高有向通信拓扑下分布式一致性算法的收敛速度,提出了一种基于有向通信拓扑的高阶分布式一致性算法。该算法通过有向单跳通信,利用有向二跳邻接节点的前多步信息提高分布式一致性算法的收敛速度。对有向通信拓扑下该算法的收敛性能和收敛速度进行了分析和仿真比较。结果显示,该算法在满足一定条件下能收敛到初始状态的平均值,与其他同样利用二跳邻接节点信息的一致性算法相比,具有通信量小、收敛速度更快的特点,但是能容忍的最大通信延时变小。     

Leader-following consensus of multiple uncertain Euler–Lagrange systems under switching network topology

In recent years, the leader-following consensus problem for multiple uncertain Euler–Lagrange systems has been studied under some restrictive assumptions on the network topology. In this paper, we further study the same problem under switching network topology. We propose a distributed adaptive control law that can solve the problem under a switching network satisfying jointly connected condition. Under this condition, our results do not require the network to be undirected and allow the network to be disconnected at any time instant. Moreover, by introducing an exosystem to generate various reference signals, our control law can handle a class of reference signals such as sinusoidal signals with arbitrary amplitudes and initial phases or ramp signals with arbitrary slopes.