Quantized Communication Research Articles

Quantized Consensus by the ADMM: Probabilistic Versus Deterministic Quantizers

This paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers (ADMM). We first study the effects of probabilistic and deterministic quantizations on a distributed ADMM algorithm. With probabilistic quantization, this algorithm yields linear convergence to the desired average in the mean sense with a bounded variance. When deterministic quantization is employed, the distributed ADMM either converges to a consensus or cycles with a finite period after a finite-time iteration. In the cyclic case, local quantized variables have the same mean over one period and hence each node can also reach a consensus. We then obtain an upper bound on the consensus error which depends only on the quantization resolution and the average degree of the network. Finally, we propose a two-stage algorithm which combines both probabilistic and deterministic quantizations. Simulations show that the two-stage algorithm, without picking small algorithm parameter, has consensus errors that are typically less than one quantization resolution for all connected networks where agents' data can be of arbitrary magnitudes.

Quantized Iterative Learning Consensus Tracking of Digital Networks With Limited Information Communication.

This brief investigates the quantized iterative learning problem for digital networks with time-varying topologies. The information is first encoded as symbolic data and then transmitted. After the data are received, a decoder is used by the receiver to get an estimate of the sender's state. Iterative learning quantized communication is considered in the process of encoding and decoding. A sufficient condition is then presented to achieve the consensus tracking problem in a finite interval using the quantized iterative learning controllers. Finally, simulation results are given to illustrate the usefulness of the developed criterion.

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.

Analyses on Target Tracking under Quantized Communication

In the paper, we address the problem of target tracking with quantized communication. While the probabilistic distributed function of the measurement is unknown, in order to simplify the calculations of target tracking system and improve the accuracy of estimation, we propose a Kalman filter under uniformly probabilistic quantization, and analyze the performance of the probabilistic quantization Kalman filter. Simulations results are provided to verify the performance of the target tracking system under uniformly probabilistic quantization.

Pseudo Two-Hop Distributed Consensus with Adaptive Quantization

In order to improve the accuracy and the convergence rate of distributed consensus under quantized communication, in the paper, based on adaptive quantization scheme, we propose the pseudo two-hop distributed consensus algorithm. By analyses and simulations, Results show that the pseudo two-hop distributed consensus algorithm based on adaptive quantization can reach an average consensus, and its convergence rate is higher than that of the first-order adaptive quantized distributed consensus algorithm, moreover, the mean square errors are smaller within the finite steps.

Average consensus of continuous‐time multi‐agent systems with quantized communication

SUMMARYThis paper focuses on the average consensus problem of first‐order and second‐order continuous‐time multi‐agent systems with logarithmic quantized information transmission. The balanced and strongly connected digraphs are utilized to characterize the interaction topologies between agents. Based on the state estimation, distributed state updating mechanisms are introduced for every agent such that all agents’ states achieve average consensus asymptotically. By means of differential inclusion theory, we discuss the existence and convergence property of the Krasovskii solutions to the closed‐loop system models. By designing the proper control gain parameters and quantizer accuracy, two sufficient conditions are established to guarantee the achievement of average consensus. Finally, two numerical simulations are provided to illustrate the effectiveness of theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Gossip Consensus Algorithm Based on Time-Varying Influence Factors and Weakly Connected Graph for Opinion Evolution in Social Networks

We provide a new gossip algorithm to investigate the problem of opinion consensus with the time-varying influence factors and weakly connected graph among multiple agents. What is more, we discuss not only the effect of the time-varying factors and the randomized topological structure but also the spread of misinformation and communication constrains described by probabilistic quantized communication in the social network. Under the underlying weakly connected graph, we first denote that all opinion states converge to a stochastic consensus almost surely; that is, our algorithm indeed achieves the consensus with probability one. Furthermore, our results show that the mean of all the opinion states converges to the average of the initial states when time-varying influence factors satisfy some conditions. Finally, we give a result about the square mean error between the dynamic opinion states and the benchmark without quantized communication.

Quantized Data--Based Distributed Consensus under Directed Time-Varying Communication Topology

Distributed average consensus (DAC) is investigated for multiagent systems (MASs) with directed time-varying communication topology and quantized communication data. We propose a communication feedback--based distributed consensus protocol suitable for directed time-varying topologies to deal with the inconsistency between the internal state of each agent's encoder and the output of its neighbors' decoder, and give rigorous analysis for the consensus of the MAS. The consensus protocols are designed based on uniform quantizers with scaling. A finite lower bound of the communication data rate between each pair of adjacent agents is obtained to ensure the exponential consensus by properly choosing system parameters. In addition, the lower bound is proved to be merely 1-bit for the directed fixed topology case, no matter how large the agent number is. A numerical example is presented to demonstrate the results obtained.

Pseudo Multi-Hop Distributed Consensus with Adaptive Quantization

The convergence accuracy of distributed consensus with quantization communication depends on the quantization error and the convergence rate of the distributed consensus algorithm. In order to improve the accuracy and the convergence rate of distributed consensus under quantized communication, in the paper, based on the adaptively quantized scheme, we propose the pseudo multi-hop adaptively quantized distributed consensus algorithm. We analyze the convergence performance of the pseudo multi-hop adaptively quantized distributed consensus algorithm, and the algorithm can achieves a consensus in a mean square sense. Simultaneously, Simulations are present. Results show that the pseudo multi-hop adaptively quantized distributed consensus algorithm can reach an average consensus, and its convergence rate is higher than those of the other adaptive quantized distributed consensus algorithms.

High-Order Distributed Consensus with One-Bit Adaptive Quantization

The convergence performance of distributed consensus algorithm with adaptive quantization communication depends on the convergence rate of the distributed consensus algorithm. In order to improve the convergence performance of distributed consensus under adaptive quantization communication, based on the one-bit adaptive quantization scheme, we propose the high-order distributed consensus to update the state of every node. We analyze the convergence performance and calculate the mean square error of the high-order distributed consensus algorithm with one-bit adaptive quantization. The high-order distributed consensus with one-bit adaptive quantization achieves a consensus in a mean square sense. Simultaneously, Simulations are done about the high-order distributed consensus based on one-bit adaptive quantization. Results show that the high-order distributed consensus algorithm based on one-bit adaptive quantization can reach an average consensus, and its convergence rate is higher than those of the first-order adaptive quantized distributed consensus algorithm and second-order adaptive quantized distributed consensus algorithm.

Distributed dual averaging method for multi-agent optimization with quantized communication

In this paper we propose a distributed dual averaging method for solving the constrained multi-agent optimization problem, in which multiple agents try to cooperatively optimize the sum of their local convex objective functions subject to a global convex constraint set over a network. We consider two cases: (i) The communications among agents are perfect, and (ii) The communications among agents are deterministically or probabilistically quantized. In the first case, we provide a way to control the convergence performance of the proposed method through adjusting the number of consensus iterations we run in the subgradient step. In the second case, we consider two kinds of quantizers, and provide bounds on their convergence rates to highlight the dependence on the quantization resolutions respectively. Finally, we provide a numerical example to show the effectiveness of the proposed methods.

Average consensus with weighting matrix design for quantized communication on directed switching graphs

SUMMARYWe study average consensus for directed graphs with quantized communication under fixed and switching topologies. In the presence of quantization errors, conventional consensus algorithms fail to converge and may suffer from an unbounded asymptotic mean square error. We develop robust consensus algorithms to reduce the effect of quantization. Specifically, we introduce a robust weighting matrix design and use the H ∞ performance index to measure the sensitivity from the quantization error to the consensus deviation. Linear matrix inequalities are used as design tools. The mean square deviation is proven to converge and its upper bound is explicitly given in the case of fixed topology with probabilistic quantization. Numerical results demonstrate the effectiveness of this method. Copyright © 2012 John Wiley & Sons, Ltd.

Quantized Consensus of Multi‐Agent Systems Via Broadcast Gossip Algorithms

AbstractDistributed 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 Quantized Averaging under Directed Time-Varying Topologies

AbstractFor multi-agent systems with directed and time-varying communication graph and limited quantized communication data rate, distributed average consensus is investigated. We first give the corresponding convergence results for the case of directed fixed communication network, and then, propose a feedback-based distributed consensus protocol for the time-varying topology case to deal with the inconsistency between the internal state of each agent's encoder and the output of its neighbors’ decoder. It is shown that if the communication graph is directed, balanced and periodically connected, then exponential average consensus can be achieved by using merely one bit information exchange between each pair of adjacent agents at each time step.

Quantized tracking control for a multi‐agent system with high‐order leader dynamics

AbstractThis paper presents a study of a tracking control problem for a multi‐agent system with an active leader and quantized communication constraints. We first design a discrete‐time distributed estimator‐based tracking control for each follower‐agent and analyze the tracking convergence with the help of the Riccati equation and common Lyapunov function when the communication channel is perfect and the interconnection topology is time‐varying. Then a stochastic quantization strategy is applied to model the information communication in the agent coordination and the corresponding solution to the tracking control problem is also given. Finally, a numerical example is given to illustrate the tracking control algorithm.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control

The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.

Gossip consensus algorithms via quantized communication

This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise “gossip” communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.

Optimal strategies in the average consensus problem

Let a set of communicating agents compute the average of their initial positions, where every agent is restricted to communicate to a given small number of other agents (average consensus problem). We prove that the optimal topology of communication is given by a de Bruijn graph. Consensus is then reached in finitely many steps. This solution is valid when the number of agents is an exact power of the out-degree of the communication graph. We introduce an algebraic tool, the shifted Kronecker product, and a more general family of strategies, also based on a de Bruijn communication graph. Those strategies are compared to Cayley strategies in terms of the speed of convergence. We also show that quantized communication between the agents still allows finite convergence, to a consensus, which is not in general the average of the initial positions.

Average consensus on networks with quantized communication

AbstractThis work presents a contribution to the solution of the average agreement problem on a network with quantized links. Starting from the well‐known linear diffusion algorithm, we propose a simple and effective adaptation that is able to preserve the average of states and to drive the system near to the consensus value, when a uniform quantization is applied to communication between agents. The properties of this algorithm are investigated both by a worst‐case analysis and by a probabilistic analysis, and are shown to depend on the spectral properties of the evolution matrix. A special attention is devoted to the issue of the dependence of the performance on the number of agents, and several examples are given. Copyright © 2008 John Wiley & Sons, Ltd.

A Low Complexity Euclidean Norm Approximation

The need for real-time computation of the Euclidean norm of a vector arises frequently in many signal processing applications such as vector median filtering, vector quantization and multiple-input multiple-output wireless communication systems. In this correspondence, we examine the properties of a linear combination of the 1-norm and the infinity norm as an approximation to the Euclidean norm of real-valued vectors. The approximation requires only two multiplications regardless of the vector length and does not require sorting of the absolute values of the vector entries. Numerical results show that the considered approximation incurs negligible performance degradations in typical applications.