Average Consensus Protocol Research Articles

A new finite-time average consensus protocol with boundedness of convergence time for multi-robot systems

Multi-robot consensus has been extensively applied in robotics. In this study, a new protocol is proposed to solve the finite-time average consensus problem. The protocol can improve the convergence rate. The upper bound of the convergence time is obtained. Analysis shows that there exists a limit value of the convergence time when the disagreement of initial states tends to be infinitely large, and the value is irrelevant to the initial states. The relationship between convergence time and initial states, communication topology, parameter is analysed. Lastly, the effectiveness of the results is verified by simulations.

A novel finite-time average consensus protocol based on event-triggered nonlinear control strategy for multiagent systems

We present a novel finite-time average consensus protocol based on event-triggered control strategy for multiagent systems. The system stability is proved. The lower bound of the interevent time is obtained to guarantee that there is no Zeno behavior. Moreover, the upper bound of the convergence time is obtained. The relationship between the convergence time and protocol parameter with initial state is analyzed. Lastly, simulations are conducted to verify the effectiveness of the results.

Privacy in Distributed Average Consensus

Distributed average consensus refers to computing average of inputs held by multiple agents communicating with each other over peer-to-peer network. Cooperation amongst agents is imperative for any distributed average consensus protocol as each agent has to share its input with other agents, which are usually the adjacent(neighboring) agents. That being said, privacy issues could discourage some agents from participating in such protocols. This paper proposes a novel distributed privacy mechanism that preserves privacy of the collection of honest agents’ inputs as long as the colluding semi-honest agents do not form a vertex cut. The proposed privacy mechanism does not alter the average of agents’ inputs, hence it does not provide privacy against what is already lost by knowing the average of the inputs. It poses minimal additional computation and communication costs, requires no alteration of the distributed consensus protocol and promises a highly scalable practical solution for privacy in distributed average consensus. The privacy achieved is quantified using Kullback-Leibler divergence (KL-divergence) and limitations are discussed analytically for two cases; case i) inputs are continuous random variables, and case ii) inputs are discrete random variables.

Bipartite Linear χ‐Consensus of Double‐Integrator Multi‐Agent Systems With Measurement Noise

AbstractThe bipartite consensus problem is investigated for double‐integrator multi‐agent systems in the presence of measurement noise. A distributed protocol with time‐varying consensus gain is proposed. By using tools of state transition matrix and algebraic graph theory, necessary and sufficient conditions for the designed protocol to be a mean square bipartite linear χ‐consensus protocol are given. It is shown that the signed digraph being structurally balanced and having a spanning tree are not only sufficient, but also necessary for bipartite consensus. Furthermore, the protocol is proved to be a mean square bipartite average consensus protocol if the signed graph is weight balanced.

A novel finite-time average consensus protocol for multi-agent systems with switching topology

Multi-agent consensus has been widely applied in engineering. A novel protocol that can achieve an average state consensus for multi-agent systems in finite time is presented in this paper. The proposed protocol contains a non-linear and a linear term. The state consensus is achieved in finite time by the non-linear term and convergence performance is improved by the linear term to some degree. The protocol can be applied to systems with a switching topology as long as the communication graph is always undirected and connected. The upper bound of convergence time is obtained. The relationship between convergence time and protocol parameter, communication topology and initial state is analysed. Lastly, simulations are conducted to verify the effectiveness of the results.

Game Design and Analysis for Price-Based Demand Response: An Aggregate Game Approach.

In this paper, an aggregate game is adopted for the modeling and analysis of energy consumption control in smart grid. Since the electricity users' cost functions depend on the aggregate energy consumption, which is unknown to the end users, an average consensus protocol is employed to estimate it. By neighboring communication among the users about their estimations on the aggregate energy consumption, Nash seeking strategies are developed. Convergence properties are explored for the proposed Nash seeking strategies. For energy consumption game that may have multiple isolated Nash equilibria, a local convergence result is derived. The convergence is established by utilizing singular perturbation analysis and Lyapunov stability analysis. Energy consumption control for a network of heating, ventilation, and air conditioning systems is investigated. Based on the uniqueness of the Nash equilibrium, it is shown that the players' actions converge to a neighborhood of the unique Nash equilibrium nonlocally. More specially, if the unique Nash equilibrium is an inner Nash equilibrium, an exponential convergence result is obtained. Energy consumption game with stubborn players is studied. In this case, the actions of the rational players can be driven to a neighborhood of their best response strategies by using the proposed method. Numerical examples are presented to verify the effectiveness of the proposed methods.

Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error (MSE) of subspace-based estimators is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations.

Consensus of discrete-time linear multi-agent systems with Markov switching topologies and time-delay

This paper investigates the average consensus problems of the discrete-time linear multi-agent systems (LMAS) with Markov switching topologies. The average consensus protocol is a time-delay feedback switching controller. Compared with existing controllers, it is switching with time-delay. The constant time-delay exists in the signal feedback, and the time-varying time-delay exists in the state feedback. Firstly, we introduce a concept of the average consensus in this stochastic system. Then, we develop a new signal mode to simplify this challenging problem. By Lyapunov technique, two LMIs determinate theorems of average consensus are provided. Then we can find a controller to solve such problems effectively by these theorems. And the last theorem also reveals that we can determinate consensus by the maximum and minimum nonzero eigenvalues of the Laplacian matrices. Finally, a numerical example is given to illustrate the efficiency of our results.

Closed-form solution for optimal convergence speed of multi-agent systems with discrete-time double-integrator dynamics for fixed weight ratios

This paper considers the convergence speed of multi-agent systems with discrete-time double-integrator dynamics. The communication topology is assumed to be fixed and undirected. The speed of convergence of the associated average consensus protocol is analyzed, and the problem of maximizing the convergence speed over the free parameters in the consensus protocol is considered. A closed-form solution to this problem is proposed assuming that the ratios of weights of communication links are fixed. Furthermore it is shown that when the weight ratios are considered as decision variables, a global optimum of the convergence speed can be obtained by solving an LMI problem. Simulation results are provided that demonstrate the effectiveness of the proposed approach.

Distributed average consensus in multi-agent networks with limited bandwidth and time-delays

This paper studies the distributed average consensus problem of multi-agent digital networks with time-delays. For the network, each agent can only exchange symbolic data with its neighbours. We provide a distributed average consensus protocol which uses the quantized and time-delay information. We consider two types of dynamic encoders/decoders in our protocol. One uses inverse proportion function as scaling function, while the other uses exponential function as scaling function. All agents can reach average consensus asymptotically with our protocol. Furthermore, we show that the average consensus protocol is robust to finite symmetric time-delays, but is sensitive to asymmetric time-delays that will destroy the average consensus of the networks. Finally, simulations are presented to illustrate validity of our theoretical results.

Average Consensus Problems in Networks of Agents with Fixed and Switching Topology and Unknown Control Direction

This paper is devoted to the average consensus problems in directed networks of agents with unknown control direction. In this paper, by using Nussbaum function techniques and Laplacian matrix, novel average consensus protocols are designed for multiagent systems with unknown control direction in the cases of directed networks with fixed and switching topology. In the case of switching topology, the disagreement vector is utilized. Finally, simulation is provided to demonstrate the effectiveness of our results.

Distributed quantized consensus for agents on directed networks

Communication bandwidth and network topology are two important factors that affect performance of distributed consensus in multi-agent systems. The available works about quantized average consensus assume that the adjacency matrices associated with the digraphs are doubly stochastic, which amounts to that the digital networks are balanced. However, this assumption may be unrealistic in practice. In this paper, without assuming double stochasticity, the authors revisit an existing quantized average consensus protocol with the logarithmic quantization scheme, and investigate the quantized consensus problem in general directed digital networks that are strongly connected but not necessarily balanced. The authors first derive an achievable upper bound of the quantization precision parameter to design suitable logarithmic quantizer, and this bound explicitly depends on network topology. Subsequently, by means of the matrix transformation and the Lyapunov techniques, the authors provide a testable condition under which the weighted average consensus can be achieved with the proposed quantized protocol.

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.

Time Synchronization in Wireless Sensor Networks Using Max and Average Consensus Protocol

This paper proposes a novel distributed time synchronization scheme for wireless sensor networks, which uses max consensus to compensate for clock drift and average consensus to compensate for clock offset. The main idea is to achieve a global synchronization just using local information. The proposed protocol has the advantage of being totally distributed, asynchronous, and robust to packet drop and sensor node failure. Finally, the protocol has been implemented in MATLAB. Through several simulations, we can see that this protocol can reduce clock error to ±10 ticks, adapt to dynamic topology, and be suitable to large-scale applications.

Distributed Design of Finite-time Average Consensus Protocols

In this paper, we are interested in the finite-time average consensus problem for multi-agent systems or wireless sensor networks. This issue is formulated in a discrete-time framework by utilizing a linear iteration scheme, where each node repeatedly updates its value as a weighted linear combination of its own value and those of its neighbors. Unlike most of research in literature, this work deals with the foremost step, called configuration step, during which the consensus protocol is to be set up in each agent. Designing consensus protocols can be viewed as a matrix factorization problem. For connected undirected graphs, we propose a learning method for solving such matrix factorization problem in a distributed way. More precisely, we first show how solving this problem for the particular case of strongly regular graphs. Then, a distributed gradient back-propagation algorithm is derived for the general case. The performance of the proposed algorithm is evaluated by means of simulation results.

Quantized consensus on first-order integrator networks

This paper studies the quantized average consensus problem of first-order integrator agents with connected undirected communication graphs. Because quantized data is inherently associated with discrete-time measurements, a sampled-data based average consensus protocol is proposed, in which each agent uses the quantized states of its neighbors measured synchronously at sampling times to update its own state. It is proved that for a connected network, the distance between the individual state and the average of initial states becomes smaller than the quantization step size in finite time, provided the sampling size is smaller than a constant depending on the degree of the communication topology. When the sampling size tends to zero, an asynchronous protocol is investigated, in which the limitation of the switching frequency of quantizers is considered. It is shown that for a connected network, the given protocol drives the state of each agent into a neighborhood of the average of initial states, provided the dwell-time of quantizers is small enough.

Distributed Weight Selection in Consensus Protocols by Schatten Norm Minimization

In this work we study the weight optimization problem for average consensus protocols by reformulating it as a Schatten norm minimization with parameter p. We show that as p approaches infinity, the optimal solution of the Schatten norm induced problem recovers the optimal solution of the original problem. Moreover, by tuning the parameter p in our proposed minimization, we can simply trade-off the quality of the solution (i.e., the speed of convergence) for communication/computation requirements (in terms of number of messages exchanged and volume of data processed). We then propose a distributed algorithm to solve the Schatten norm minimization and we show that it outperforms the other distributed weight selection methods.

Event-triggered average-consensus of multi-agent systems with weighted and direct topology

This paper investigates the average-consensus problem of multi-agent systems with direct and weighted topologies. Event-triggered control laws are adopted so as to reduce the frequency of individual control updating since the agents may be resource-limited in many real systems. The discrete time instants where the events are triggered are determined by a trigger function with respect to a certain measurement error. A centralized average-consensus protocol is proposed first for networks with fixed interaction topology, the stability and influencing factors of which are also analyzed. The design of trigger functions for networks with variable topology is also discussed. Then the results are extended to the decentralized counterpart, in which agents require only the information of their neighbors. Numerical examples are also provided that demonstrate the effectiveness of the theoretical results.

Consensus-based decentralized clustering for cooperative spectrum sensing in cognitive radio networks

A large number of previous works have demonstrated that cooperative spectrum sensing (CSS) among multiple users can greatly improve detection performance. However, when the number of secondary users (SUs; i.e., spectrum sensors) is large, the sensing overheads (e.g., time and energy consumption) will likely be intolerable if all SUs participate in CSS. In this paper, we proposed a fully decentralized CSS scheme based on recent advances in consensus theory and unsupervised learning technology. Relying only on iteratively information exchanges among one-hop neighbors, the SUs with potentially best detection performance form a cluster in an ad hoc manner. These SUs take charge of CSS according to an average consensus protocol and other SUs outside the cluster simply overhear the sensing outcomes. For comparison, we also provide a decentralized implementation of the existing centralized optimal soft combination (OSC) scheme. Numerical results show that the proposed scheme has detection performance comparable to that of the OSC scheme and outperforms the equal gain combination scheme and location-awareness scheme. Meanwhile, compared with the OSC scheme, the proposed scheme significantly reduces the sensing overheads and does not require a priori knowledge of the local received signal-to-noise ratio at each SU.

Necessary and Sufficient Conditions for Consensus of Double-Integrator Multi-Agent Systems With Measurement Noises

An average consensus protocol is proposed for continuous-time double-integrator multi-agent systems with measurement noises under fixed topologies. The time-varying control gain is employed to attenuate noises. The closed-loop system is therefore a time-varying linear stochastic differential equation. By determining the state transition matrix of this closed-loop system, the dynamic characteristics of the multi-agent system can be fully described. It is proved that in the noisy communication environment the average consensus can be achieved if and only if the communication topology is a balanced and strongly connected graph, and the time-varying control gain satisfies the stochastic approximation-type conditions. Under the proposed protocol, the position of each agent is convergent in mean square to a common random variable whose mathematical expectation is the average of initial positions and initial velocities of all agents in the system, while each agent's velocity is convergent in mean square to a common random variable whose mathematical expectation and variance are both zero.