Showing papers on "Consensus published in 2012"

Cooperative Output Regulation of Linear Multi-Agent Systems

Abstract: In this technical note, we consider the cooperative output regulation of linear multi-agent systems. The overall system consists of two groups of subsystems. While the first group of subsystems can access the exogenous signal, the second cannot. As a result, the problem cannot be solved by the decentralized approach. By devising a distributed observer, we can solve the problem by a dynamic full information distributed control scheme. The problem can also be viewed as a generalization of some results of the leader-following consensus problem of multi-agent systems.

Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach

Abstract: A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept.

A Necessary and Sufficient Condition for Consensus Over Random Networks

Abstract: We consider the consensus problem for stochastic discrete time linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1.

Cooperative Output Regulation With Application to Multi-Agent Consensus Under Switching Network

Abstract: In this paper, we consider the cooperative output regulation of linear multi-agent systems under switching network. The problem can be viewed as a generalization of the leader-following consensus problem of multi-agent systems. Due to the limited information exchanges of different subsystems, the problem cannot be solved by the decentralized approach and is not allowed to be solved by the centralized control. By devising a distributed observer network, we can solve the problem by both dynamic state feedback control and dynamic measurement output feedback control. As an application of our main result, we show that a special case of our results leads to the solution of the leader-following consensus problem of linear multi-agent systems.

Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems

Abstract: In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected.

Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case

Abstract: This technical note presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponentially, and obtain lower and upper bounds on their convergence rates in terms of the network topologies, problem characteristics, and algorithm parameters, including the algebraic connectivity, Laplacian spectral radius, and function curvatures. The findings of this technical note may be regarded as a natural generalization of several well-known algorithms and results for distributed consensus, to distributed convex optimization.

Differentially private iterative synchronous consensus

Abstract: The iterative consensus problem requires a set of processes or agents with different initial values, to interact and update their states to eventually converge to a common value. Protocols solving iterative consensus serve as building blocks in a variety of systems where distributed coordination is required for load balancing, data aggregation, sensor fusion, filtering, and synchronization. In this paper, we introduce the private iterative consensus problem where agents are required to converge while protecting the privacy of their initial values from honest but curious adversaries. Protecting the initial states, in many applications, suffice to protect all subsequent states of the individual participants.We adapt the notion of differential privacy in this setting of iterative computation. Next, we present (i) a server-based and (ii) a completely distributed randomized mechanism for solving differentially private iterative consensus with adversaries who can observe the messages as well as the internal states of the server and a subset of the clients. Our analysis establishes the tradeoff between privacy and the accuracy: for given e, b >0, the e-differentially private mechanism for N agents, is guaranteed to convergence to a value within O(⁄1/e √bN) of the average of the initial values, with probability at least (1-b).

Consensus Clock Synchronization for Wireless Sensor Networks

Abstract: Wireless sensor networks (WSN) are emerging as a valuable tool in many fields of science and industry. Time synchronization is an important issue for WSN's due to the collaborative and distributed nature of the tasks they perform. This paper describes a new technique for clock synchronization in WSNs called consensus clock synchronization that provides internal synchronization to a virtual consensus clock. It is sensitive to the limited resources available to sensor nodes and is robust to many of the challenges faced in dynamic ad-hoc networks. Simulations are presented to analyse the effectiveness of the synchronization protocol in a mesh network.

Group consensus of multi-agent systems with directed information exchange

Abstract: We discuss a new consensus problem – a group consensus problem – in networks of dynamic agents. For a complex network consisting of several sub-networks owing to physical quantities or task distributions, it is concerned with this case that the agents in a sub-network share a consistent value while there is no agreement between any two sub-networks. When the information exchange is directed, a novel consensus protocol is designed to solve the group consensus problem. The convergence analysis is discussed and several criteria are established based on graph theories and matrix theories. Simulation results are presented to demonstrate the effectiveness of the theoretical results.

Finite-Time Consensus for Leader-Following Second-Order Multi-Agent Networks

Abstract: This paper studies the leader-following finite-time consensus problem for the second-order multi-agent networks with fixed and switched topologies. Based on the graph theory, matrix theory, homogeneity with dilation and LaSalle's invariance principle, finite-time consensus protocols are designed by the pinning control technique without assuming that the interaction graph is connected or the leader is globally reachable. Moreover, the control protocol of each agent using local information is presented, and some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.

Consensus of heterogeneous multi-agent systems without velocity measurements

Abstract: This article considers the consensus problem of heterogeneous multi-agent system composed of first-order and second-order agents, in which the second-order integrator agents cannot obtain the velocity (second state) measurements for feedback. Two different consensus protocols are proposed. First, we propose a consensus protocol and discuss the consensus problem of heterogeneous multi-agent system. By applying the graph theory and the Lyapunov direct method, some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader-following networks. Second, due to actuator saturation, we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi-agent system. Finally, some examples are presented to illustrate the effectiveness of the obtained criterions.

Robustness of information diffusion algorithms to locally bounded adversaries

Abstract: We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in its neighborhood. We introduce a topological property known as r-robustness of a graph, and show that this property provides improved bounds on tolerating malicious behavior, in comparison to traditional concepts such as connectivity and minimum degree. We use this topological property to analyze the canonical problems of distributed consensus and broadcast, and provide sufficient conditions for these operations to succeed. Finally, we provide a construction for r-robust graphs and show that the common preferential-attachment model for scale-free networks produces a robust graph.

Differentially Private Iterative Synchronous Consensus

Abstract: The iterative consensus problem requires a set of processes or agents with different initial values, to interact and update their states to eventually converge to a common value. Protocols solving iterative consensus serve as building blocks in a variety of systems where distributed coordination is required for load balancing, data aggregation, sensor fusion, filtering, clock synchronization and platooning of autonomous vehicles. In this paper, we introduce the private iterative consensus problem where agents are required to converge while protecting the privacy of their initial values from honest but curious adversaries. Protecting the initial states, in many applications, suffice to protect all subsequent states of the individual participants. First, we adapt the notion of differential privacy in this setting of iterative computation. Next, we present a server-based and a completely distributed randomized mechanism for solving private iterative consensus with adversaries who can observe the messages as well as the internal states of the server and a subset of the clients. Finally, we establish the tradeoff between privacy and the accuracy of the proposed randomized mechanism.

Consensus and its ℒ 2 -gain performance of multi-agent systems with intermittent information transmissions

Abstract: This article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network, where each agent can only communicate with its neighbours intermittently. A class of control algorithms is first introduced, using only intermittent relative local information. By combining tools from switching systems and Lyapunov stability theory, some sufficient conditions are established for consensus of multi-agent systems without any external disturbances under a fixed strongly connected topology. Theoretical analyses are further provided for consensus of multi-agent systems in the presence of external disturbances. It is shown that a finite ℒ2-gain performance index for the closed-loop multi-agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology. The results are then extended to consensus ...

Sampled-data based average consensus with logarithmic quantizers

Abstract: This paper considers the sampled-data average consensus problem for multi-agent systems with first order continuous dynamics. The communication channels among the agents are constrained in which the exchanged information is digital rather than analogue. In this paper, the logarithmic quantizer is applied to the communication channels. A distributed consensus protocol is proposed based on sampled measurements. It is proved that as long as the quantization levels are dense enough, the proposed protocol is robust to the logarithmic quantization, i.e. all the states of the agents are uniformly bounded and the gap between the state of each agent and the average value of the initial conditions converges to zero as the density of quantization levels goes to infinity. An example is given to demonstrate the effectiveness of the protocol.

Distributed Consensus on Robot Networks for Dynamically Merging Feature-Based Maps

Abstract: In this paper, we study the feature-based map merging problem in robot networks. While in operation, each robot observes the environment and builds and maintains a local map. Simultaneously, each robot communicates and computes the global map of the environment. Communication between robots is range-limited. We propose a dynamic strategy, based on consensus algorithms, that is fully distributed and does not rely on any particular communication topology. Under mild connectivity conditions on the communication graph, our merging algorithm, asymptotically, converges to the global map. We present a formal analysis of its convergence rate and provide accurate characterizations of the errors as a function of the timestep. The proposed approach has been experimentally validated using real visual information.

Necessary and Sufficient Conditions for Consensus of Delayed Fractional-order Systems

Abstract: In this paper, we study the consensus problem of fractional-order systems with input delays. Using Laplace transform method, the stability of the fractional-order systems is first discussed in the frequency domain. Based on the generalized Nyquist stability criterion, a necessary and sufficient condition is further derived to ensure the consensus of fractional-order systems with identical input delays over directed interaction topology. Furthermore, when the interaction topology is undirected, the consensus condition of fractional-order systems with heterogeneous input delays is explicitly given. Finally, some illustrative examples are presented to show the effectiveness and advantages of the theoretical results.

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

Abstract: 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.

Global $H_\infty$ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics

Abstract: This study addresses the global consensus problems of a class of non-linear multi-agent systems with Lipschitz non-linearity and directed communication graphs, by using a distributed consensus protocol based on the relative states of neighbouring agents. A two-step algorithm is presented to construct a protocol, under which a Lipschitz multi-agent system without disturbances can reach global consensus for a strongly connected directed communication graph. Another algorithm is then given to design a protocol that can achieve global consensus with a guaranteed H∞ performance for a Lipschitz multi-agent system subject to external disturbances. The case with a leader–follower communication graph is also discussed. Finally, the effectiveness of the theoretical results is demonstrated through a network of single-link manipulators.

Vulnerability and protection for distributed consensus-based spectrum sensing in cognitive radio networks

Abstract: Cooperative spectrum sensing is key to the success of cognitive radio networks. Recently, fully distributed cooperative spectrum sensing has been proposed for its high performance benefits particularly in cognitive radio ad hoc networks. However, the cooperative and fully distributed natures of such protocol make it highly vulnerable to malicious attacks, and make the defense very difficult. In this paper, we analyze the vulnerabilities of distributed sensing architecture based on a representative distributed consensus-based spectrum sensing algorithm. We find that such distributed algorithm is particularly vulnerable to a novel form of attack called covert adaptive data injection attack. The vulnerabilities are even magnified under multiple colluding attackers. We further propose effective protection mechanisms, which include a robust distributed outlier detection scheme with adaptive local threshold to thwart the covert adaptive data injection attack, and a hash-based computation verification approach to cope with collusion attacks. Through simulation and analysis, we demonstrate the destructive power of the attacks, and validate the efficacy and efficiency of our proposed protection mechanisms.

Distributed H ∞ consensus of multi-agent systems: a performance region-based approach

Abstract: This article addresses the distributed H ∞ consensus problem of multi-agent systems with general linear node dynamics using relative output measurements. The notion of H ∞ consensus performance region is first introduced and then analysed as a basis for the protocol design. A new kind of distributed observer-type H ∞ protocols is further proposed. Theoretical analysis indicates that the distributed H ∞ consensus problem can be solved if and only if the coupling strength of the protocol belongs to the H ∞ performance region of the closed-loop network. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Convergence Speed of Binary Interval Consensus

Abstract: We consider the convergence time for solving the binary consensus problem using the interval consensus algorithm proposed by B\' en\' ezit, Thiran and Vetterli (2009). In the binary consensus problem, each node initially holds one of two states and the goal for each node is to correctly decide which one of these two states was initially held by a majority of nodes. We derive an upper bound on the expected convergence time that holds for arbitrary connected graphs, which is based on the location of eigenvalues of some contact rate matrices. We instantiate our bound for particular networks of interest, including complete graphs, paths, cycles, star-shaped networks, and Erd\" os-R\' enyi random graphs; for these graphs, we compare our bound with alternative computations. We find that for all these examples our bound is tight, yielding the exact order with respect to the number of nodes. We pinpoint the fact that the expected convergence time critically depends on the voting margin defined as the difference between the fraction of nodes that initially held the majority and the minority states, respectively. The characterization of the expected convergence time yields exact relation between the expected convergence time and the voting margin, for some of these graphs, which reveals how the expected convergence time goes to infinity as the voting margin approaches zero. Our results provide insights into how the expected convergence time depends on the network topology which can be used for performance evaluation and network design. The results are of interest in the context of networked systems, in particular, peer-to-peer networks, sensor networks and distributed databases.