Consensus seeking over directed networks with limited information communication

Existing works that deal with the problem of distributed average consensus with quantized information communication assume that the update matrices are doubly stochastic, which amounts to agents evolving on balanced directed networks with digital channels. This paper is concerned with the problem of seeking consensus via quantized information communication over a general unbalanced directed digital network. It is established that, by designing a protocol with a finite-level uniform quantization scheme, merely one bit quantized information transmitted along each connected digital channel suffices for achieving weighted average consensus with an exponential convergence rate, as long as the directed unbalanced network is strongly connected. An explicit characterization of the convergence rate of consensus is also given. By avoiding the double stochasticity assumption on the update matrix, the proposed quantized protocol is particularly suitable for the scenarios where no bidirectional and/or balanced information communication among agents is available.     

Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions

In this paper, average-consensus control is considered for networks of continuous-time integrator agents under fixed and directed topologies. The control input of each agent can only use its local state and the states of its neighbors corrupted by white noises. To attenuate the measurement noises, time-varying consensus gains are introduced in the consensus protocol. By combining the tools of algebraic graph theory and stochastic analysis, the convergence of these kinds of protocols is analyzed. Firstly, for noise-free cases, necessary and sufficient conditions are given on the network topology and consensus gains to achieve average-consensus. Secondly, for the cases with measurement noises, necessary and sufficient conditions are given on the consensus gains to achieve asymptotic unbiased mean square average-consensus. It is shown that under the protocol designed, all agents’ states converge to a common Gaussian random variable, whose mathematical expectation is just the average of the initial states.     

多智能体时滞网络的加权平均一致性

提出了线性和非线性分布式协调控制器,使多智能体系统取得加权平均一致性.对于线性控制器,考虑网络存在通信时间延迟的情形,给出了能容忍的最大固定时滞的一个紧凑上界.考虑网络结点控制输入的有界约束,给出了一类非线性分布式控制器的收敛性分析.结果说明,网络的连通性是系统取得一致性的关键.最后对时滞网络的情形给出了仿真示例.     

A hybrid systems model for power control in multicell wireless data networks

We present a power control scheme based on noncooperative game theory, using a fairly broad class of convex cost functions. The multicell CDMA wireless data network is modeled as a switched hybrid system where handoffs of mobiles between different cells correspond to discrete switching events between different subsystems. Under a set of sufficient conditions, we prove the existence of a unique Nash equilibrium for each subsystem, and prove global exponential stability of an update algorithm. We also establish the global convergence of the dynamics of the multicell power control game to a convex superset of Nash equilibria for any switching (handoff) scheme satisfying a mild condition on average dwell-time. Robustness of these results to feedback delays as well as to quantization is investigated. In addition, we consider a quantization scheme to reduce the communication overhead between mobiles and the base stations. Finally, we illustrate the power control scheme developed through simulations.     

Consensus of single integrator multi-agent systems with directed topology and communication delays

In this paper, a distributed control scheme has been developed for consensus of single integrator multi-agent systems with directed fixed communication topology for arbitrarily large constant, time-varying or distributed communication delays. It is proved that the closed loop control system can reach consensus with an exponential convergence rate if and only if the topology is quasi-strongly connected. Simulation results are also provided to demonstrate the effectiveness of the proposed controller.     

无线传感器网络生存期优化体系研究

提出了系统设计全生命周期的网络生存期优化体系模型,该模型利用先验统计信息将不同的应用与优化算法统一起来,并以评估结果作为反馈调节网络使之达到网络生存期最大限度的优化;构建了一种优化体系的具体评估模型,利用网络能耗分布量化具体应用服务需求,使用网络能量分布度量网络服务能力,并通过量化结果计算网络能量浪费的上限;给出了一种网络密度调节方法,用以发现有利于生存期优化的网络密度分布规律,并对该方法的收敛性以及解的有效性进行了理论证明.模拟实验结果表明该评估模型和密度调节方法可以有效控制网络能耗分布,发现有利于延长网络生存期的密度规律,从而验证了网络生存期优化体系的有效性.     

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.     

Distributed dynamic consensus under quantized communication data

Distributed dynamic average consensus is investigated under quantized communication data. We use a uniform quantizer with constant quantization step‐size to deal with the saturation caused by the dynamic consensus error and propose a communication feedback‐based distributed consensus protocol suitable for directed time‐varying topologies to make the internal state of each agent's encoder consistent with the output of its neighbors' decoder. For the case where the communication topology is directed, balanced and periodically connected, it is shown that if the difference of the reference inputs satisfies some boundedness condition, then the designed quantized dynamic consensus protocol can ensure the states of all the agents achieve dynamic average consensus with arbitrarily small steady state error by properly choosing system parameters. The lower bound of the required quantization levels and the method to choose the system parameters are also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

A decentralized MAC protocol for opportunistic spectrum access in cognitive wireless networks

Cognitive MAC protocols are designed to efficiently utilize the scarce spectral resources without affecting the performance characteristics of primary users. The use of spectrum opportunities can often require stochastic approaches due to difficulty in predicting their appearance. Infrastructure based coordinated access techniques are not viable for many applications and spectrum bands, especially in the case of wireless local area and sensor networks. In this article, we describe CogMAC, a decentralized cognitive MAC protocol, which is based on the multichannel preamble reservation scheme. The protocol dynamically selects an available communication channel using a distributed channel selection scheme and allows nodes to be completely asynchronous to each other. CogMAC does not require a common control channel or a cooperative infrastructure. The MAC design addresses practical issues such as network dynamics and traffic awareness. We have carried out the performance evaluation of our CogMAC protocol on Wireless Open Access Research Platform (WARP) SDR testbed. Experimental results indicate that our protocol is able to achieve reliable data communication by opportunistically utilizing the available spectrum holes even in harshly interfering environments.     

Quantized consensus over directed networks with switching topologies

This paper studies the quantized consensus problem for a group of agents over directed networks with switching topologies. We propose an effective distributed protocol with an adaptive finite-level uniform quantized strategy, under which consensus among agents is guaranteed with weaker communication conditions. In particular, we analytically prove that each agent sending 5-level quantized information to each of its neighbors, together with 3-level quantized information to itself at each time step, which suffices for attaining consensus with an exponential convergence rate as long as the duration of all link failures in the directed network is bounded. By dropping the typical common left eigenvector requirement for the existence of common quadratic Lyapunov function, we conduct the convergence analysis based on the notion of input-to-output stability. The proposed quantized protocol has favorable merits of requiring little communication overhead and increasing robustness to link unreliability, and it fits well into the digital network framework.     

Prediction and congestion control algorithm for networked motion tracking

In this paper a novel prediction method and a communication protocol is proposed for distributed motion tracking systems, for example robot control system over the Internet based on on-line visual information. It is assumed that the trajectory generator part of the control system is connected to the low level controller through wide area network (WAN). In this case the variable network delay, packet losses, irregular packet arrival can severely influence the control characteristics (transient behavior and tracking performance) in a negative sense. The proposed prediction method is based on dynamic filters and it generates the trajectory on the control system side in the control periods when no new information on the time varying reference trajectory arrives through the network. The developed application level communication protocol is meant to keep the packet loss under a predefined limit even if the network bandwidth varies below the value required by the control application. Simulations and real-time experiments show that the prediction algorithm applied jointly with the proposed communication protocol can effectively compensate the effect of networked communication on control characteristics.     

带事件触发机制的分布式量化随机无梯度投影算法

本文研究多智能体系统的分布式约束优化问题,系统中的每个智能体仅知道自身的局部目标函数和全局非空约束集,通过与邻居节点进行信息交互,最终协同求出优化问题的最优解.本文所提出的算法针对通信网络为时变不平衡有向图,且每个智能体不知道它的出度的情况.同时考虑到现实中通信带宽有限和通讯成本的限制,应用基于编译码方案的量化技术对节点之间的通讯信息进行预处理,再利用事件触发广播技术降低网络的通信次数.同时引入高斯光滑函数和随机无梯度方法替代传统的次梯度方法.本文提出了基于事件触发的分布式量化随机无梯度算法,在目标函数为凸且Lipschitz连续的条件下,证明了所提算法能收敛到最优值的邻域,同时给出了使量化器不饱和量化水平更新规则.最后通过数值仿真验证了算法的有效性和可行性.     

多个体切换网络分布式量化次梯度优化算法

由于已有的分布式次梯度算法大多基于理想的假设：网络拓扑是有向平衡的,构成网络的个体间通信的是各个个体某个状态变量的完全精确的信息。针对更一般的非平衡切换网络以及实际生活中网络通道的带宽限制,提出一种基于有限量化信息通信的切换网络分布式量化次梯度优化算法。在非平衡切换网络中,通过设计具有有限量化水平的一致量化器使所有信息在发送之前都经过量化,利用非二次李雅普诺夫函数方法,证明了所提出的多个体分布式量化次梯度优化算法的收敛性。最后仿真实例验证了所提算法的有效性,而且通过调节量化水平参数,在相同的带宽条件下,可提高信息传输速率,使网络中的个体更快地达到一致。该方法弱化了对刻画网络拓扑的邻接矩阵的假设及对网络带宽的要求,更具实用性。     

Distributed edge event‐triggered consensus protocol of multi‐agent systems with communication buffer

This paper proposes a distributed edge event‐triggered (DEET) scheme of multi‐agent systems via a communication buffer to reduce unnecessary update of controllers induced by fast information transmission. This edge scheme avoids a synchronous phenomenon in node event‐triggered mechanism, in which the triggering of one agent activates information transmission of all edges linked with this agent. Hence, the node event‐triggered scheme leads to unnecessary update of control protocols while the DEET provides a new approach without constrains on synchronous phenomenon of edge information exchange. That is, the communication on each edge is independent with other edges. In addition, we investigate another case where edge information transmission is subject to quantization and a quantized edge event‐triggered control protocol is proposed. Note that such a quantized protocol guarantees asymptotical consensus instead of bounded consensus in most of the existing literature. Meanwhile, both DEET and quantized edge event‐triggered schemes have nontrivial properties of excluding Zeno behavior. Furthermore, an algorithm is provided to avoid continuous event detection; hence, the communication traffic of the whole network is reduced significantly. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus problems in networks of agents with switching topology and time-delays

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.     

Event‐triggered distributed constrained consensus

We consider a distributed consensus problem for continuous‐time multi‐agent systems with set constraints on the final states. To save communication costs, an event‐triggered communication‐based protocol is proposed. By comparing its own instantaneous state with the one previously broadcasted to neighbours, each agent determines the next communication time. Based on this event‐triggered communication, each agent is not required to continuously monitor its neighbours' state and the communication only happens at discrete time instants. We show that, under some mild conditions, the constrained consensus of the multi‐agent system with the proposed protocol can be achieved with an exponential convergence rate. A lower bound of the transmission time intervals is provided that can be adjusted by choosing different values of parameters. Numerical examples illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Second-order consensus of multi-agent systems with noises via intermittent control

Second-order consensus of multi-agent systems with noises via intermittent control is investigated in this paper. First, we study the mean-square consensus problem with communication noises by intermittent control. In order to reach consensus, under the strong directed interacted topology, by using the tools of graph theory and Lyapunov method, a distributed control protocol is proposed based on the noises and periodical intermittent information. The upper bound of noise strength in the sense of matrix norm and the lower bound of communication time duration are obtained. Second, a class of coupled system models which include delay-terms in their nonlinearities in the noisy environment is discussed. Under the balanced strongly connected topology, the sufficient conditions to achieve the mean-square average-consensus are obtained. Finally, simulations are given to illustrate the effectiveness of our results.     

Average Convergence for Directed & Undirected Graphs in Distributed Systems

Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems. This has fascinated numerous scientific groups for their promising applications as they have the freedom to achieve their local and global goals and make their own decisions. Network communication topologies based on graph and matrix theory are widely used in a various real-time applications ranging from software agents to robotics. Therefore, while sustaining the significance of both directed and undirected graphs, this research emphases on the demonstration of a distributed average consensus algorithm. It uses the harmonic mean in the domain of multi-agent systems with directed and undirected graphs under static topologies based on a control input scheme. The proposed agreement protocol focuses on achieving a constant consensus on directional and undirected graphs using the exchange of information between neighbors to update their status values and to be able to calculate the total number of agents that contribute to the communication network at the same time. The proposed method is implemented for the identical networks that are considered under the directional and non-directional communication links. Two different scenarios are simulated and it is concluded that the undirected approach has an advantage over directed graph communication in terms of processing time and the total number of iterations required to achieve convergence. The same network parameters are introduced for both orientations of the communication graphs. In addition, the results of the simulation and the calculation of various matrices are provided at the end to validate the effectiveness of the proposed algorithm to achieve consensus.     

工业以太网协议EtherNet/IP

工业以太网已经成为控制系统网络发展的主要方向。文中所介绍的EtherNet／IP协议是一种优良的工业以太网方案。由于它采用了CIP协议及新的生产者／消费者的通信模式，使得控制网络设备能够更有效地传输数据，更容易与Internet／Intranet集成。同时，它是一种面向对象和开放性的控制网络方案。采用这种方案的控制网络具有较好的一致性，能够解决控制网络中互操作的难题。     

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.