In this brief paper, a new consensus protocol based on the sign of innovations is proposed. Based on this protocol each agent only requires single-bit of information about its relative state to its neighboring agents. This is significant in real-time applications, since it requires less computation and/or communication load on agents. Using Lyapunov stability theorem the convergence is proved for networks having a spanning tree. Further, the convergence is shown to be in finite-time, which is significant as compared to most asymptotic protocols in the literature. Time-variant network topologies are also considered in this paper, and final consensus value is derived for undirected networks. Applications of the proposed consensus protocol in (i) 2D/3D rendezvous task, (ii) distributed estimation, (iii) distributed optimization, and (iv) formation control are considered and significance of applying this protocol is discussed. Numerical simulations are provided to compare the protocol with the existing protocols in the literature.
We consider a multi-agent consensus problem in the presence of adversarial agents. The adversaries are able to listen to the inter-agent communications and try to estimate the state of the agents. The agents have a limited bit-rate for communication and are required to quantize the transmitted signal in order to meet the bit-rate constraint of the communication channel. We propose a consensus protocol that is protected against the adversaries, i.e., the expected mean-square error of the adversary state estimate is lower bounded. In order to deal with the bit-rate constraint, we propose a dynam…
This paper addresses the robust consensus problem under switching topologies. Contrary to existing methods, the proposed approach provides decentralized protocols that achieve consensus for networked multi-agent systems in a predefined time. Namely, the protocol design provides a tuning parameter that allows setting the convergence time of the agents to a consensus state. An appropriate Lyapunov analysis exposes the capability of the current proposal to achieve predefined-time consensus over switching topologies despite the presence of bounded perturbations. Finally, the paper presents a compa…
Gossip protocols are popular methods for average consensus problems in distributed computing. We prove new convergence guarantees for a variety of such protocols, including path, clique, and synchronous pairwise gossip. These arise by exploiting the connection between these protocols and the block randomized Kaczmarz method for solving linear systems. Moreover, we extend existing convergence results for block randomized Kaczmarz to allow for a more general choice of blocks, rank-deficient systems, and provide a tighter convergence rate guarantee. We furthermore apply this analysis to inconsist…
In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic convergence of these algorithms pose a challenge in the practical settings where the response from agents is required in finite time. To this end, we propose a Maximum-Minimum protocol which propagates the global maximum and minimum values of agent states (while running consensus algorithm) in the network. We establish that global maximum and minimum values are str…
Average consensus theory is intensely popular for building time synchronization in wireless sensor network (WSN). However, the average consensus-based time synchronization algorithm is based on iteration that pose challenges for efficiency, as they entail high communication cost and long convergence time in large-scale WSN. Based on the suggestion that the greater the algebraic connectivity leads to the faster the convergence, a novel multi-hop average consensus time synchronization (MACTS) is developed with innovative implementation in this paper. By employing multi-hop communication model, i…
Institut de Matemàtica Multidisciplinària, Universitat Politècnica de València（多学科数学研究所，瓦伦西亚理工大学）；Departament de Sistemes Informàtics i Computació, Universitat Politècnica de València（信息系统与计算系，瓦伦西亚理工大学）
We address the problems of bearing-only consensus and formation control, where each agent can only measure the relative bearings of its neighbors and relative distances are not available. We provide stability results for the Filippov solutions of two gradient-descent laws from non-smooth Lyapunov functions in the context of differential inclusion. For the consensus and formation control problems with undirected sensing topologies, we prove finite-time and asymptotic convergence of the proposed non-smooth gradient flows. For the directed consensus problem, we prove asymptotic convergence using …
This work addresses the problem of distributed formation tracking for a group of follower holonomic mobile robots around a reference signal. The reference signal is comprised of the geometric center of the positions of multiple leaders. This work's main contribution is a novel Modulated Distributed Virtual Observer (MDVO) for the reference signal. Moreover, the proposed MDVO is based on an exact dynamic consensus algorithm with a prescribed convergence time. In addition, we provide simulation examples showcasing two different application scenarios for the proposal.
This paper presents new classes of consensus protocols with fixed-time convergence, which enable the definition of an upper bound for consensus state as a parameter of the consensus protocol, ensuring its independence from the initial condition of the nodes. We demonstrate that our methodology subsumes current classes of fixed-time consensus protocols that are based on homogeneous in the bi-limit vector fields. Moreover, the proposed framework enables for the development of independent consensus protocols that are not needed to be homogeneous in the bi-limit. This proposal offers extra degrees…
Max-Consensus with Deterministic Convergence in Directed Graphs with Unreliable Communication Links
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；University of Cyprus（塞浦路斯大学）；Aalto University（阿尔托大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
A Global Convergence Analysis of Consensus ALADIN for Convex Optimization
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；North China University of Water Resources and Electric Power（华北水利水电大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
We revisit an algorithm for distributed consensus optimization proposed in 2010 by J. Wang and N. Elia. By means of a Lyapunov-based analysis, we prove input-to-state stability of the algorithm relative to a closed invariant set composed of optimal equilibria and with respect to perturbations affecting the algorithm's dynamics. In the absence of perturbations, this result implies linear convergence of the local estimates and Lyapunov stability of the optimal steady state. Moreover, we unveil fundamental connections with the well-known Gradient Tracking and with distributed integral control. Ov…
Previous researches have shown that adding local memory can accelerate the consensus. It is natural to ask questions like what is the fastest rate achievable by the $M$-tap memory acceleration, and what are the corresponding control parameters. This paper introduces a set of effective and previously unused techniques to analyze the convergence rate of accelerated consensus with $M$-tap memory of local nodes and to design the control protocols. These effective techniques, including the Kharitonov stability theorem, the Routh stability criterion and the robust stability margin, have led to the f…
Fully distributed consensus control for stochastic multi-agent systems under undirected and directed topologies
China University of Geosciences（中国地质大学）；Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems（复杂系统先进控制与智能自动化湖北省重点实验室）
We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired compression ratio. The proposed method provably reduces the communication overhead on the network at every communication round. Contrary to existing literature, we allow for arbitrary compression ratios in the communicated messages. We show a linear convergence rate for the proposed method on the consensus problem. Moreover, we provide explicit convergence rates for …
Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated via experimental data. Numerical studies also indicate that this new mechanism recreates some non-trivial real-world features of opinion evolution. In this paper, we conduct a thorough theoretical analysis of the weighted-median opinion dynamics. We fully characterize the set of all equilibria, and we establish the almost-sure finite-time convergence for any…
This paper investigates the fixed-time consensus problem for a class of multi-agent systems with simple dynamics. Unlike the traditional way to realize fixed-time convergence, a novel strategy using the property of periodic functions is proposed to achieve fixed-time convergence. On this basis, novel protocols for achieving fixed-time consensus and fixed-time average consensus are then given, where the upper bound of the consensus time is independent of initial conditions. Moreover, the result of fixed-time average consensus is extended to a more general case, where the weights of different st…
A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics, which we name the No one left behind dynamics, is the introduction of a local control on the agents which preserves the connectivity of the interaction network. We rigorously demonstrate that these dynamics result in unconditional convergence to a consensus. The qualitative nature of our argument prevents us quantifying how fast a conse…
On Convergence Rate of Leader-Following Consensus of Linear Multi-Agent Systems with Communication Noises
State Key laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所复杂系统管理与控制国家重点实验室）；Department of Electrical and Computer Engineering, University of California, Riverside（加州大学河滨分校电气与计算机工程系）
Distributed and Decentralized Optimization Algorithms via Consensus ALADIN
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；University of Pittsburgh（匹兹堡大学）；KTH Royal Institute of Technology（皇家理工学院）；Digital Futures（数字未来）
Characterizing Trust and Resilience in Distributed Consensus for Cyberphysical Systems
Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气工程与计算机科学系）；School of Electrical, Computer and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）；Computer Science Department at the School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院计算机科学系）
Texas A&M University（德克萨斯农工大学）；University of Minnesota（明尼苏达大学）
We study the convergence properties of Riemannian gradient method for solving the consensus problem (for an undirected connected graph) over the Stiefel manifold. The Stiefel manifold is a non-convex set and the standard notion of averaging in the Euclidean space does not work for this problem. We propose Distributed Riemannian Consensus on Stiefel Manifold (DRCS) and prove that it enjoys a local linear convergence rate to global consensus. More importantly, this local rate asymptotically scales with the second largest singular value of the communication matrix, which is on par with the well-k…
We study a finite and fixed relative formation of possibly mobile wireless networked nodes. The nodes apply average consensus to agree on a common value like the formation's center. %Performance of consensus in terms of convergence speed is affected by message losses due path loss and interference. We assume framed slotted ALOHA based broadcast communication. Our work has two contributions. First, we analyze outage correlation of random media access in wireless networks under Nakagami fading. Second, the correlation terms are applied to the so called L2-joint spectral and numerical radii to an…
