Consensus of multiple double‐integrator agents with intermittent measurement

This paper is concerned with consensus problems in directed networks of multiple agents with double‐integrator dynamics. It is assumed that each agent adjusts its state based on the information of its states relative to its neighbors at discrete times and the interaction topology among agents is time‐varying. Both synchronous and asynchronous cases are considered. The synchrony means that each agent's update times, at which it obtains new control signals, are the same as the others', and the asynchrony implies that each agent's update times are independent of the others'. In the synchronous case, the consensus problem is proved to be equivalent to the asymptotic stability problem of a discrete‐time switched system. By analyzing the asymptotic stability of the discrete‐time switched system, it is shown that consensus can be reached if the update time intervals are small sufficiently, and an allowable upper bound of update time intervals is obtained. In the asynchronous case, the consensus problem is transformed into the global asymptotic stability problem of a continuous‐time switched system with time‐varying delays. In virtue of a linear matrix inequality method, it is proved that consensus can be reached if the delays are small enough, and an admissible upper bound of delays is derived. Simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Event‐triggered Control for Cluster Consensus in Multi‐agent Networks

This paper considers the issue of cluster consensus for multiple agents in fixed and undirected networks. Agents in a network are supposed to split into several clusters, and a fraction of the agents in each cluster are pinned by virtual leaders. According to the Lyapunov stability theory and graph theory, some appropriate event‐triggered protocols are developed for consensus of the agents belonging to the same cluster, which can greatly reduce both the number of communication updates and that of control actuation updates. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed theoretical results.     

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.     

多智能体切换网络自适应组一致性

在切换网络下,针对具有未知且互不相同的非线性动态的多智能体系统,假设其未知的非线性动态可线性参数化,并运用自适应控制策略和牵制控制方法,提出了一种组一致性算法,使得多智能体系统在切换网络下达到组一致性。该算法仅仅依赖相邻智能体间的相对位置信息,基于Lyapunov理论、Barbalat引理、自适应控制理论及代数图论等理论,对该算法进行了稳定性分析和参数收敛分析。通过一个仿真实例验证了提出的算法有效性。     

Group consensus control for double‐integrator dynamic multiagent systems with fixed communication topology

The problem of group consensus is investigated in this paper, where all agents possess double‐integrator dynamics. Two different kinds of consensus protocols are proposed for networks with fixed communication topology to reach group consensus for the agents’ positions and velocities. Convergence analysis is discussed, and necessary and/or sufficient conditions are presented for multiagent systems to achieve group consensus. The first protocol leads to dynamic consensus where positions of all agents reach time‐varying consensus values. By applying the second protocol, both the agents’ positions and their velocities reach constant consensus values. That is, static consensus is achieved. Simulation examples are given to show the effectiveness of the theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed Consensus of Multi‐Agent Networks Via Event‐Triggered Pinning Control

This paper is concerned with distributed consensus between two multi‐agent networks with the same topology structure. Considering one network as the leaders' network and the other one as the followers' network, a new event‐triggered pinning control scheme is proposed to realize distributed consensus between these two networks. By utilizing the graph theory and Lyapunov functional method, consensus criteria are derived in the form of linear matrix inequalities. Moreover, distributed consensus of multi‐agent networks with Lipschitz nonlinear dynamics is also discussed. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.     

Group consensus tracking of second-order nonlinear multi-agent systems with time-varying reference velocities

This paper investigates group consensus tracking problems with time-varying reference velocities. The multiple agents are described as second-order nonlinear dynamics in directed information exchange settings. For the multi-agent networks formed by finite agent groups, novel distributed protocols with/without time-varying transmission delays are designed to solve the group consensus tracking problems. The problems are first transformed into the asymptotical stability of consensus error systems and the input-to-state stability of tracking error systems, and then sufficient conditions are derived to guarantee the agents realizing the group consensus tracking based on Lyapunov stability theories. Finally, several simulations are given to verify the effectiveness of the theoretical results.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Distributed δ-consensus in directed delayed networks of multi-agent systems

In this article, we propose a distributed δ-consensus protocol in directed networks of dynamic agents having communication delays. The δ-consensus protocol is an average consensus protocol where agents exchange the information with their neighbours at some discontinuous moments. We provide convergence analysis for such consensus algorithm under stochastic switching communication graphs, and then present some generic criteria for solving the average consensus problem. We also show that directed delayed networks of dynamic agents can achieve average consensus even when each agent in the networks intermittently exchanges the information with its neighbours only at some discrete moments. Subsequently, a typical numerical example illustrates and visualises the effectiveness and feasibility of the theoretical results.     

On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs

ABSTRACT

This paper aims to analyse the stability of a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks composed of agents with first-order dynamics. In particular, in the analysed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittency in the communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an essential feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. Simulations illustrate the performance of the proposed consensus algorithms. In the presented scenarios, results show that the settling time of the considered algorithms grows slower than other consensus algorithms for dynamic networks as the number of nodes increases.     

Cluster-delay consensus in multi-agent systems via pinning leader-following approach with intermittent effect

In this paper, the cluster consensus problem with delays of first-order nonlinear multi-agent systems is studied through pinning leader-following approach with periodic intermittent effect. The graph of the networked system is assumed to be directed and weakly connected. A new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link, specifically, the agents in each cluster are divided into three subsets due to the orientation of their topological degree, and each subset of agents is controlled by an individual law. A redefined notion on cluster consensus with two sorts of time delays is proposed in this article. Some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay, while agents in different clusters reach consensus with delays via following their leaders. Some numerical simulations are given to illustrate the effectiveness of the theoretical results.     

Stability analysis and controller design for consensus in discrete-time networks with heterogeneous agent dynamics

In this paper, we study the heterogeneous consensus problem in directed networks consisting of first- and second-order agents that can only receive the position states of their neighbors. Necessary and sufficient conditions on the controller parameters are obtained in order to achieve consensus in the network. The mathematical expressions of the consensus equilibria are given for two different scenarios. Furthermore, we propose a systematic method for choosing controller parameters to ensure stability in a network of agents with heterogeneous dynamics. Several numerical examples are also provided to illustrate the theoretical results.     

Quantized Consensus of Multi‐Agent Systems Via Broadcast Gossip Algorithms

Distributed consensus problems of multi‐agent systems on directed networks are studied in this paper. For the communication of agents, it is assumed that only one agent can be selected with a prescribed probability, and it broadcasts its own state to neighbors via quantized communication (for any arbitrary quantization) at each time step. For this kind of communication, the fundamental questions are how to design distributed algorithms and what kinds of network topology together lead to the quantized consensus. A class of broadcast gossip algorithms is proposed, and a necessary and sufficient graphical condition is given to ensure the quantized consensus. In particular, the obtained graphical condition does not require a symmetric network topology, which is weaker than those in some other literature. Several numerical simulations are given to show the effectiveness of the proposed algorithms.     

Distributed model predictive control for consensus of nonlinear second‐order multi‐agent systems

This paper proposes a distributed model predictive control algorithm for the consensus of nonlinear second‐order multi‐agent systems. At each update time, all the agents are permitted to optimize. A positively invariant terminal region and a corresponding auxiliary controller are developed for each agent. Furthermore, time‐varying compatibility constraint is presented to denote a degree of consistency between the assumed trajectories and the actual trajectories of each agent. Given the designed terminal ingredients (terminal region, auxiliary controller, and terminal cost) and compatibility constraints, the recursive feasibility and closed‐loop stability of the whole system are guaranteed. The simulation results are given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Leader‐following consensus for nonlinear agents with measurement feedback

The leader‐following consensus problem is investigated for large classes of nonlinear identical agents. Sufficient conditions are provided for achieving consensus via state and measurement feedback laws based on a local (ie, among neighbors) information exchange. The leader's trajectories are assumed bounded without knowledge of the containing compact set and the agents' trajectories possibly unbounded under the action of a bounded input. Generalizations to heterogeneous agents and robustness are also discussed.     

多智能体系统基于自适应控制下的二分-分量一致性

二分-分量一致性是指网络系统中部分具有相似特性智能体的某些分量随时间推移趋于相同的值,而剩余智能体的某些分量则随时间趋于相反的值,是一种弱于恒同一致和二分一致的动力学行为.为此,对符号网络上非线性多智能体系统的二分-分量一致性问题展开研究.首先,针对多智能体系统中各智能体之间存在的合作关系或竞争关系,设计有效的自适应牵制控制器;随后,基于Lyapunov稳定性理论和矩阵理论,导出该非线性系统二分-分量一致性得以实现的充分条件;最后,通过数值模拟验证理论结果.     

Leader-follower consensus control of Lipschitz nonlinear systems by output feedback

This paper deals with the leader-follower consensus problem of Lipschitz nonlinear systems under fixed directed communication networks. Both state and output feedback control are proposed based on state and output measurements of neighbouring agents, respectively. Laplacian matrix features are explored for the stability analysis, and the sufficient conditions are derived to solve the consensus problem. Finally, simulation results are included to demonstrate the effectiveness of the output-based consensus controller.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

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.