Time Synchronization in WSNs: A Maximum-Value-Based Consensus Approach
TL;DR: The weighted maximum time synchronization (WMTS), which is able to counteract the impact of random communication delays, is proposed, which can synchronize the clock skew completely in expectation and achieve acceptable synchronization accuracy.
Abstract: This paper considers time synchronization in wireless sensor networks. When the communication delay is negligible, the maximum time synchronization (MTS) protocol is proposed by which the skew and offset of each node can be synchronized simultaneously. For a more practical case where the intercommunication delays between each connected node are positive random variables, we propose the weighted maximum time synchronization (WMTS), which is able to counteract the impact of random communication delays. Despite the clock offset that cannot be synchronized, WMTS can synchronize the clock skew completely in expectation and achieve acceptable synchronization accuracy. For both protocols, we provide rigorous proofs of global convergence as well as the upper bounds of their convergence time. Compared with existing consensus-based synchronization protocols, the main advantages of our protocols include: 1) a faster convergence speed so that the synchronization can be achieved in a finite time for MTS, and in a finite time in expectation for WMTS, respectively; 2) simultaneous synchronization of both skews and offsets; and 3) random communication delays can be handled effectively. Numerical examples are presented to demonstrate the effectiveness of the proposed protocols.
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TL;DR: This paper studies leader-follower synchronization in heterogeneous dynamic networks via distributed impulsive control to drive the followers to approximately synchronize with the leader within a nonzero error bound, referred to as quasi-synchronization.
329 citations
TL;DR: It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems.
Abstract: This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master–slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.
247 citations
TL;DR: A consensus-based algorithm is designed to solve the problem of distributed energy management for both generation and demand side in smart grid by taking transmission losses into account and it is proved the convergence and optimality of the proposed algorithm is achieved.
Abstract: This paper investigates the problem of distributed energy management for both generation and demand side in smart grid. Different from existing works, we formulate a social welfare maximization problem for a more practical scenario by taking transmission losses into account. The formulated problem is non-convex due to the non-convexity of the power balance equality constraint caused by the transmission losses. To solve the problem, we first transform the equality constraint into an inequality constraint and obtain a new convex optimization problem. We then derive a sufficient condition to guarantee that the new problem has the same solution as the original one. Because of the coupling in the constraint, Lagrange duality method is adopted to decompose the problem. Considering the general communication topology among generators and demands, i.e., directed connected topology, we design a consensus-based algorithm to solve the problem in a distributed way. We also prove the convergence and optimality of the proposed algorithm, under which the social welfare maximization is achieved. Extensive simulations validate the theoretical results and demonstrate the effectiveness of the proposed algorithm.
236 citations
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Abstract: Fog computing is a new computing architecture, composed of a set of near-user edge devices called fog nodes, which collaborate together in order to perform computational services such as running ap...
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Cites methods from "Time Synchronization in WSNs: A Max..."
...To solve this first sub-problem, a convex optimization technique was applied (He et al. 2014)....
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TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
11,658 citations
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...Giridhar and Kumar [10] formulated DTSC as a coordinate-descent optimization problem....
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05 Mar 2007
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Abstract: This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations
9,715 citations
"Time Synchronization in WSNs: A Max..." refers background in this paper
...The main idea is that the algorithm elects a root node and then the root node periodically floods its current time into the tree network....
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TL;DR: This work analyzes the averaging problem under the gossip constraint for an arbitrary network graph, and finds that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm.
Abstract: Motivated by applications to sensor, peer-to-peer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of "gossip" algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the so-called Preferential Connectivity (PC) model.
2,634 citations
"Time Synchronization in WSNs: A Max..." refers background in this paper
...It should be noted that all three of these algorithms need a reference node or root node....
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09 Dec 2002
TL;DR: Reference Broadcast Synchronization (RBS) as discussed by the authors is a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts, and receivers use their arrival time as a point of reference for comparing their clocks.
Abstract: Recent advances in miniaturization and low-cost, low-power design have led to active research in large-scale networks of small, wireless, low-power sensors and actuators. Time synchronization is critical in sensor networks for diverse purposes including sensor data fusion, coordinated actuation, and power-efficient duty cycling. Though the clock accuracy and precision requirements are often stricter than in traditional distributed systems, strict energy constraints limit the resources available to meet these goals.We present Reference-Broadcast Synchronization, a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts. A reference broadcast does not contain an explicit timestamp; instead, receivers use its arrival time as a point of reference for comparing their clocks. In this paper, we use measurements from two wireless implementations to show that removing the sender's nondeterminism from the critical path in this way produces high-precision clock agreement (1.85 ± 1.28μsec, using off-the-shelf 802.11 wireless Ethernet), while using minimal energy. We also describe a novel algorithm that uses this same broadcast property to federate clocks across broadcast domains with a slow decay in precision (3.68 ± 2.57μsec after 4 hops). RBS can be used without external references, forming a precise relative timescale, or can maintain microsecond-level synchronization to an external timescale such as UTC. We show a significant improvement over the Network Time Protocol (NTP) under similar conditions.
2,537 citations
03 Nov 2004
TL;DR: The FTSP achieves its robustness by utilizing periodic flooding of synchronization messages, and implicit dynamic topology update and comprehensive error compensation including clock skew estimation, which is markedly better than that of the existing RBS and TPSN algorithms.
Abstract: Wireless sensor network applications, similarly to other distributed systems, often require a scalable time synchronization service enabling data consistency and coordination. This paper describes the Flooding Time Synchronization Protocol (FTSP), especially tailored for applications requiring stringent precision on resource limited wireless platforms. The proposed time synchronization protocol uses low communication bandwidth and it is robust against node and link failures. The FTSP achieves its robustness by utilizing periodic flooding of synchronization messages, and implicit dynamic topology update. The unique high precision performance is reached by utilizing MAC-layer time-stamping and comprehensive error compensation including clock skew estimation. The sources of delays and uncertainties in message transmission are analyzed in detail and techniques are presented to mitigate their effects. The FTSP was implemented on the Berkeley Mica2 platform and evaluated in a 60-node, multi-hop setup. The average per-hop synchronization error was in the one microsecond range, which is markedly better than that of the existing RBS and TPSN algorithms.
2,267 citations
Additional excerpts
...(Corresponding author: P. Cheng.)...
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