Showing papers on "Consensus published in 2014"

Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies

Abstract: Distributed consensus tracking is addressed in this paper for multi-agent systems with Lipschitz-type node dynamics. The main contribution of this work is solving the consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. By using tools from M-matrix theory, a class of consensus tracking protocols based only on the relative states among neighboring agents is designed. By appropriately constructing Lyapunov function, it is proved that consensus tracking in the closed-loop multi-agent systems with a fixed topology having a directed spanning tree can be achieved if the feedback gain matrix and the coupling strength are suitably selected. Furthermore, with the assumption that each possible topology contains a directed spanning tree, it is theoretically shown that consensus tracking under switching directed topologies can be achieved if the control parameters are suitably selected and the dwell time is larger than a positive threshold. The results are then extended to the case where the communication topology contains a directed spanning tree only frequently as the system evolves with time. Finally, some numerical simulations are given to verify the theoretical analysis.

Observer-Based Output Feedback Event-Triggered Control for Consensus of Multi-Agent Systems

Abstract: This paper studies the consensus problem of linear multi-agent systems via observer-based event-triggered control. Two novel observer-based event-triggered control schemes, one centralized and the other distributed, are developed. It is shown that under the proposed control protocols, consensus can be reached if the underlying communication graph of the MAS is connected. An example is finally presented to illustrate the effectiveness of the proposed control methods.

A new class of finite-time nonlinear consensus protocols for multi-agent systems

Abstract: This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.

Distributed Consensus-Based Economic Dispatch With Transmission Losses

Abstract: A distributed algorithm is presented to solve the economic power dispatch with transmission line losses and generator constraints. The proposed approach is based on two consensus algorithms running in parallel. The first algorithm is a first-order consensus protocol modified by a correction term which uses a local estimation of the system power mismatch to ensure the generation-demand equality. The second algorithm performs the estimation of the power mismatch in the system using a consensus strategy called consensus on the most up-to-date information. The proposed approach can handle networks of different size and topology using the information about the number of nodes which is also evaluated in a distributed fashion. Simulations performed on standard test cases demonstrate the effectiveness of the proposed approach for both small and large systems.

Adaptive Consensus of Multi-Agent Systems With Unknown Identical Control Directions Based on A Novel Nussbaum-Type Function

Abstract: This note addresses the adaptive consensus problem of first-order and second-order linearly parameterized multi-agent systems with unknown identical control directions. First, we propose a new Nussbaum-type function based on which a key lemma is established. The lemma plays an important role in analyzing the consensus of the closed-loop multi-agent systems. Second, the Nussbaum-type function is used to design adaptive control laws for first-order and second-order linearly parameterized multi-agent systems so that each agent seeks for the unknown control direction adaptively and cooperatively. Then, under the assumption that the interconnection topology is undirected and connected, it is proved that the first-order and second-order multi-agent systems can achieve consensus by choosing proper design parameters. Two simulation examples are given to illustrate the effectiveness of the proposed control laws.

Cooperative Control of Multi-Agent Systems: A Consensus Region Approach

Abstract: Distributed controller design is generally a challenging task, especially for multi-agent systems with complex dynamics, due to the interconnected effect of the agent dynamics, the interaction graph among agents, and the cooperative control laws. Cooperative Control of Multi-Agent Systems: A Consensus Region Approach offers a systematic framework for designing distributed controllers for multi-agent systems with general linear agent dynamics, linear agent dynamics with uncertainties, and Lipschitz nonlinear agent dynamics. Beginning with an introduction to cooperative control and graph theory, this monograph: Explores the consensus control problem for continuous-time and discrete-time linear multi-agent systems Studies the H∞ and H2 consensus problems for linear multi-agent systems subject to external disturbances Designs distributed adaptive consensus protocols for continuous-time linear multi-agent systems Considers the distributed tracking control problem for linear multi-agent systems with a leader of nonzero control input Examines the distributed containment control problem for the case with multiple leaders Covers the robust cooperative control problem for multi-agent systems with linear nominal agent dynamics subject to heterogeneous matching uncertainties Discusses the global consensus problem for Lipschitz nonlinear multi-agent systems Cooperative Control of Multi-Agent Systems: A Consensus Region Approach provides a novel approach to designing distributed cooperative protocols for multi-agent systems with complex dynamics. The proposed consensus region decouples the design of the feedback gain matrices of the cooperative protocols from the communication graph and serves as a measure for the robustness of the protocols to variations of the communication graph. By exploiting the decoupling feature, adaptive cooperative protocols are presented that can be designed and implemented in a fully distributed fashion.

Semiglobal Observer-Based Leader-Following Consensus With Input Saturation

Abstract: This paper studies the observer-based leader-following consensus of a linear multiagent system on switching networks, in which the input of each agent is subject to saturation. Based on a low-gain output feedback method, distributed consensus protocols are developed. Under the assumptions that the networks are connected or jointly connected and that each agent is asymptotically null controllable with bounded controls and detectable, semiglobal observer-based leader-following consensus of the multiagent system can be reached on switching networks. A numerical example is presented to illustrate the theoretical results.

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

Abstract: SUMMARY 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.

A Mean Square Consensus Protocol for Linear Multi-Agent Systems With Communication Noises and Fixed Topologies

Abstract: The mean square consensus of linear multi-agent systems with communication noises is studied in this note. Each agent is modeled by a continuous-time linear time-invariant dynamics and the fixed communication topology is described by a digraph. The proposed consensus protocol is composed of two parts: the agent's own state feedback and the relative states between agent and its neighbor agents. Due to the existence of communication noises, the relative states cannot be obtained accurately. To attenuate the noise effect, a time-varying gain vector a(t)K is applied to the inaccurate relative states. It is proved that: 1) if the communication topology has a spanning tree and every node has at least one parent node, then the proposed protocol can solve the mean square consensus problem if and only if a(t) satisfies ∫0∞a(s)ds = ∞ and ∫0∞ a2(s)ds <; ∞; and all roots of the polynomial whose coefficients are the elements of vector K are in the left half complex plane; 2) if the communication topology has a spanning tree and there exists one node without any parent node, then the condition ∫0∞ a2(s)ds <; ∞ is only sufficient but not necessary; and 3) if the communication topology has no spanning tree, then the proposed protocol cannot solve the mean square consensus problem.

Constrained Consensus in Unbalanced Networks With Communication Delays

Abstract: In this note, a constrained consensus problem is studied for multi-agent systems in unbalanced networks in the presence of communication delays. Here each agent needs to lie in a closed convex constraint set while reaching a consensus. The communication graphs are directed, dynamically changing, and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length. The analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary. To tackle the loss of symmetry caused by unbalanced graphs and communication delays, a novel approach is proposed. The idea is to estimate the distance from each agent to the intersection set of all agents' constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction. It is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system. It is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded. Finally, a numerical example is included to illustrate the obtained theoretical results.

Distributed stochastic optimization and learning

Abstract: We consider the problem of distributed stochastic optimization, where each of several machines has access to samples from the same source distribution, and the goal is to jointly optimize the expected objective w.r.t. the source distribution, minimizing: (1) overall runtime; (2) communication costs; (3) number of samples used. We study this problem systematically, highlighting fundamental limitations, and differences versus distributed consensus problems where each machine has a different, independent, objective. We show how the best known guarantees are obtained by an accelerated mini-batched SGD approach, and contrast the runtime and sample costs of the approach with those of other distributed optimization algorithms.

Consensus of Networked Mechanical Systems With Communication Delays: A Unified Framework

Abstract: This technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays. The challenge lies in the unclear input-output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input. We establish a new input-output property of this linear networked system and moreover its convergent property under an external input, upon which, we establish a unified framework to resolve the consensus problem of multiple mechanical systems. The proposed consensus framework unifies/extends the existing results and in addition yields a fully cascaded closed-loop system. With Lyapunov-like analysis and frequency domain input-output analysis, we show that the proposed unified consensus control scheme ensures consensus without the integral action of the sliding vector, and scaled weighted average consensus with the integral action of the sliding vector. Simulation results are provided to demonstrate the performance of the proposed consensus schemes.

Cooperative Distributed Source Seeking by Multiple Robots: Algorithms and Experiments

Abstract: We consider the problem of source seeking using a group of mobile robots equipped with sensors for source concentration measurement. In the formulation, the robot team cooperatively estimates the gradient of the source field, moves to the source by tracing the gradient-ascending direction, and keeps a predefined formation in movement. We present two control algorithms with all-to-all and limited communications, respectively. For the case of all-to-all communication, rigorous analytic analysis proves that the formation center of the robots converges to the source in the presence of estimation errors with a bounded error, the upper bound of which is explicitly given. In the case of limited communication where centralized quantities are not available, distributed consensus filters are used to distributively estimate the centralized quantities, and then embedded in the distributed control laws. Numerical simulations are given to validate the effectiveness of the proposed approaches. Experimental results on the E-puck robot platform demonstrate satisfactory performances in a light source seeking application.

Multi-Agent Consensus With Relative-State-Dependent Measurement Noises

Abstract: In this note, the distributed consensus corrupted by relative- state-dependent measurement noises is considered. Each agent can mea- sure or receive its neighbors' state information with random noises, whose intensity is a vector function of agents' relative states. By investigating the structure of this interaction and the tools of stochastic differential equa- tions, we develop several small consensus gain theorems to give sufficient conditions in terms of the control gain, the number of agents and the noise intensity function to ensure mean square (m.s.) and almost sure (a.s.) consensus and quantify the convergence rate and the steady-state error. Especially, for the case with homogeneous communication and control channels, a necessary and sufficient condition to ensure m.s. consensus on the control gain is given and it is shown that the control gain is independent of the specific network topology, but only depends on the number of nodes and the noise coefficient constant. For symmetric measurement models, the almost sure convergence rate is estimated by the Iterated Logarithm Law of Brownian motions. Index Terms—Distributed consensus, distributed coordination, fading channel, measurement noises, multi-agent system.

Distributed ${\cal H}_{\infty}$ Consensus of Higher Order Multiagent Systems With Switching Topologies

Abstract: This brief addresses the distributed ${\cal H}_{\infty}$ consensus problem of multiagent systems with higher order linear dynamics and switching directed topologies. Without assuming that the directed communication topology is fixed or balanced, a class of distributed protocols is constructed and employed to achieve state consensus while guaranteeing a prescribed disturbance rejection objective, with both admissible exogenous disturbances and unknown initial states. By using tools from algebraic graph theory and switched systems theory, it is proven that the distributed ${\cal H}_{\infty}$ consensus in closed-loop multiagent systems with switching directed topologies can be achieved if the feedback gain matrix of the protocol is appropriately designed and the coupling strength among neighboring agents is larger than a derived positive value. Moreover, the consensus rate for the closed-loop nominal multi-agent systems is discussed.

Finite-time distributed consensus through graph filters

Abstract: We propose a new framework for distributed computation of average consensus. The presented framework leads to a systematic design of iterative algorithms that compute the consensus exactly, are guaranteed to converge in finite time, are computationally efficient, and require no online memory. We demonstrate that our approach is applicable to a broad class of networks. For remaining networks, our framework leads to the construction of approximating algorithms for consensus that are also guaranteed to compute in finite time. Our approach is inspired by graph filters introduced by the theoretical framework of signal processing on graphs.

Adaptive iterative learning control for coordination of second-order multi-agent systems

Abstract: SUMMARY In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi-agent systems with second-order dynamics and unknown time-varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi-agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.

A Distributed Consensus Algorithm for Decision Making in Service-Oriented Internet of Things

Abstract: In a service-oriented Internet of things (IoT) deployment, it is difficult to make consensus decisions for services at different IoT edge nodes where available information might be insufficient or overloaded. Existing statistical methods attempt to resolve the inconsistency, which requires adequate information to make decisions. Distributed consensus decision making (CDM) methods can provide an efficient and reliable means of synthesizing information by using a wider range of information than existing statistical methods. In this paper, we first discuss service composition for the IoT by minimizing the multi-parameter dependent matching value. Subsequently, a cluster-based distributed algorithm is proposed, whereby consensuses are first calculated locally and subsequently combined in an iterative fashion to reach global consensus. The distributed consensus method improves the robustness and trustiness of the decision process.

A distributed event-triggered scheme for discrete-time multi-agent consensus with communication delays

Abstract: This study mainly investigates the event-triggered data transmission in discrete-time multi-agent consensus problem with communication delays. A new distributed event-triggered scheme is proposed for the considered multi-agent network model. An action of the agent is triggered by an `event' which is a well-defined condition on the system state. For the proposed event-triggered protocol, the authors prove that the multi-agent network will achieve consensus asymptotically. Numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Second-order group consensus for multi-agent systems via pinning leader-following approach

Abstract: This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.

Leader-following consensus of second-order non-linear multi-agent systems with directed intermittent communication

Abstract: This study addresses leader-following consensus problems for multi-agent systems with second-order non-linear dynamics, under the assumption that each agent can only communicate with its neighbouring agents intermittently and the communication topology does not keep strongly connected or contain a spanning tree all along. Firstly, a class of distributed consensus algorithms are designed only based on the relative local intermittent information. Notions of completely and partly intermittent communication are proposed. Some sufficient conditions are derived for achieving consensus tracking under a general fixed topology with completely and partly intermittent communication. Then, as an extension, leader-following consensus tracking is studied under time-varying intermittent communication topologies. Finally, the effectiveness of the main results is illustrated by numerical simulations.