Distributed Solvers for Network Linear Equations with Scalarized Compression

In this paper, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme including a dimension compressing vector that applies to individual node states to generate a real-valued message for node communication as an inner product, and a data unfolding step in the local computations where the scalar message is plotted along the subspace generated by the compression vector. We first present a compressed average consensus flow that relies only on such scalar communication, and show that exponential convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their exponential convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel capacity requirement for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results.Comment: 8 pages, 4 figure

Impulsive Control of Dynamical Networks

Dynamical networks (DNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and man-made networks such as social networks, food networks, neural networks, WorldWideWeb, electrical power grid, etc., can be effectively modeled by DNs. The main focus of the present thesis is on delay-dependent impulsive control of DNs. To study the impulsive control problem of DNs, we firstly construct stability results for general nonlinear time-delay systems with delayed impulses by using the method of Lyapunov functionals and Razumikhin technique. Secondly, we study the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Then, a novel hybrid consensus protocol with dynamically changing interaction topologies is designed to take the time-delay into account in both the continuous-time communication among agents and the instant information exchange at discrete moments. We also study the consensus problem of networked multi-agent systems. Distributed delays are considered in both the agent dynamics and the proposed impulsive consensus protocols. Lastly, stabilization and synchronization problems of DNs under pinning impulsive control are studied. A pinning algorithm is incorporated with the impulsive control method. We propose a delay-dependent pinning impulsive controller to investigate the synchronization of linear delay-free DNs on time scales. Then, we apply the pinning impulsive controller proposed for the delay-free networks to stabilize time-delay DNs. Results show that the delay-dependent pinning impulsive controller can successfully stabilize and synchronize DNs with/without time-delay. Moreover, we design a type of pinning impulsive controllers that relies only on the network states at history moments (not on the states at each impulsive instant). Sufficient conditions on stabilization of time-delay networks are obtained, and results show that the proposed pinning impulsive controller can effectively stabilize the network even though only time-delay states are available to the pinning controller at each impulsive instant. We further consider the pinning impulsive controllers with both discrete and distributed time-delay effects to synchronize the drive and response systems modeled by globally Lipschitz time-delay systems. As an extension study of pinning impulsive control approach, we investigate the synchronization problem of systems and networks governed by PDEs

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Controlled Hopwise Averaging: Bandwidth/Energy-Efficient Asynchronous Distributed Averaging for Wireless Networks

This paper addresses the problem of averaging numbers across a wireless network from an important, but largely neglected, viewpoint: bandwidth/energy efficiency. We show that existing distributed averaging schemes have several drawbacks and are inefficient, producing networked dynamical systems that evolve with wasteful communications. Motivated by this, we develop Controlled Hopwise Averaging (CHA), a distributed asynchronous algorithm that attempts to "make the most" out of each iteration by fully exploiting the broadcast nature of wireless medium and enabling control of when to initiate an iteration. We show that CHA admits a common quadratic Lyapunov function for analysis, derive bounds on its exponential convergence rate, and show that they outperform the convergence rate of Pairwise Averaging for some common graphs. We also introduce a new way to apply Lyapunov stability theory, using the Lyapunov function to perform greedy, decentralized, feedback iteration control. Finally, through extensive simulation on random geometric graphs, we show that CHA is substantially more efficient than several existing schemes, requiring far fewer transmissions to complete an averaging task.Comment: 33 pages, 4 figure