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Author: Adel Aghajan Abdollah
Publisher:
ISBN:
Category :
Languages : en
Pages : 140
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Book Description
In this thesis, we study Distributed Averaging Dynamics and its main application, i.e. Distributed Optimization. More specifically, the results of this thesis can be divided into two main parts: 1) Ergodicity of distributed averaging dynamics, and 2) Distributed optimization over dependent random networks. First, we study both discrete-time and continuous-time time-varying distributed averaging dynamics. We show a necessary and a sufficient condition for ergodicity of such dynamics. We extend a well-known result in ergodicity of time-homogeneous (time-invariant) averaging dynamics and we show that ergodicity of a dynamics necessitates that its (directed) infinite flow graph has a spanning rooted tree. Then, we show that if groups of agents are connected using a rooted tree and the averaging dynamics restricted to each group is P* and ergodic, then the dynamics over the whole networks is ergodic. In particular, this provides a general condition for convergence of consensus dynamics where groups of agents capable of reaching consensus follow each other on a time-varying network. Then, we study the averaging-based distributed optimization solvers over random networks for both convex and strongly convex functions. We show a general result on the convergence of such schemes for a broad class of dependent weight-matrix sequences. In addition to implying many of the previously known results on this domain, our work shows the robustness of distributed optimization results to link-failure. Also, it provides a new tool for synthesizing distributed optimization algorithms. To prove our main theorems, we establish new results on the rate of convergence analysis of averaging dynamics and non-averaging dynamics over (dependent) random networks. These secondary results, along with the required martingale-type results to establish them, might be of interest to broader research endeavors in distributed computation over random networks.
Author: Adel Aghajan Abdollah
Publisher:
ISBN:
Category :
Languages : en
Pages : 140
Get Book Here
Book Description
In this thesis, we study Distributed Averaging Dynamics and its main application, i.e. Distributed Optimization. More specifically, the results of this thesis can be divided into two main parts: 1) Ergodicity of distributed averaging dynamics, and 2) Distributed optimization over dependent random networks. First, we study both discrete-time and continuous-time time-varying distributed averaging dynamics. We show a necessary and a sufficient condition for ergodicity of such dynamics. We extend a well-known result in ergodicity of time-homogeneous (time-invariant) averaging dynamics and we show that ergodicity of a dynamics necessitates that its (directed) infinite flow graph has a spanning rooted tree. Then, we show that if groups of agents are connected using a rooted tree and the averaging dynamics restricted to each group is P* and ergodic, then the dynamics over the whole networks is ergodic. In particular, this provides a general condition for convergence of consensus dynamics where groups of agents capable of reaching consensus follow each other on a time-varying network. Then, we study the averaging-based distributed optimization solvers over random networks for both convex and strongly convex functions. We show a general result on the convergence of such schemes for a broad class of dependent weight-matrix sequences. In addition to implying many of the previously known results on this domain, our work shows the robustness of distributed optimization results to link-failure. Also, it provides a new tool for synthesizing distributed optimization algorithms. To prove our main theorems, we establish new results on the rate of convergence analysis of averaging dynamics and non-averaging dynamics over (dependent) random networks. These secondary results, along with the required martingale-type results to establish them, might be of interest to broader research endeavors in distributed computation over random networks.
Author: Fabio Fagnani
Publisher: Springer
ISBN: 3319680226
Category : Technology & Engineering
Languages : en
Pages : 145
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Book Description
This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature. Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either deterministic or randomized. The theory needed for a full understanding of the models is constructed without assuming any knowledge of Markov chains or Perron–Frobenius theory. Jointly with their analysis of the convergence of averaging dynamics, the authors derive the properties of stochastic matrices. These properties are related to the topological structure of the associated graph, which, in the book’s perspective, represents the communication between agents. Special attention is paid to how these properties scale as the network grows in size. Finally, the understanding of stochastic matrices is applied to the study of other problems in multi-agent coordination: averaging with stubborn agents and estimation from relative measurements. The dynamics described in the book find application in the study of opinion dynamics in social networks, of information fusion in sensor networks, and of the collective motion of animal groups and teams of unmanned vehicles. Introduction to Averaging Dynamics over Networks will be of material interest to researchers in systems and control studying coordinated or distributed control, networked systems or multiagent systems and to graduate students pursuing courses in these areas.
Author: Angelia Nedić
Publisher:
ISBN: 9781680830408
Category : Computers
Languages : en
Pages : 116
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Book Description
This is the first tutorial to give such a concise and accessible introduction to game theory. It will be of use to all students, practitioners, and researchers looking to understand the basic concepts, models, and applications.
Author: Behrouz Touri
Publisher: Springer Science & Business Media
ISBN: 3642280021
Category : Computers
Languages : en
Pages : 152
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Book Description
The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication and sensor networks), as well as social and economic networks. The thesis provides in depth study of stability and other phenomena characterizing the limiting behavior of both deterministic and random averaging dynamics. By developing new concepts, and using the tools from dynamic system theory and non-negative matrix theory, several novel fundamental results are rigorously developed. These contribute significantly to our understanding of averaging dynamics as well as to non-negative random matrix theory. The exposition, although highly rigorous and technical, is elegant and insightful, and accompanied with numerous illustrative examples, which makes this thesis work easily accessible to those just entering this field and will also be much appreciated by experts in the field.
Author: Shreevatsa Rajagopalan
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
The question of computing average of numbers present at nodes in a network in a distributed manner using gossip or message-passing algorithms has been of great recent interest across disciplines -- algorithms, control and robotics, estimation, social networks, etc. It has served as a non-trivial, representative model for an important class of questions arising in these disciplines and thus guiding intellectual progress over the past few decades. In most of these applications, there is inherent dynamics present, such as changes in the network topology in terms of communication links, changes in the values of numbers present at nodes, and nodes joining or leaving. The effect of dynamics in terms of communication links on the design and analysis of algorithms for averaging is reasonably well understood, e.g. [14][2][8][4]. However, little is known about the effect of other forms of dynamics. In this thesis, we study the effect of such types of dynamics in the context of maintaining average in the network. Specifically, we design dynamics-aware message-passing or gossip algorithm that maintains good estimate of average in presence of continuous change in numbers at nodes. Clearly, in presence of such dynamics the best one can hope for is a tradeoff between the accuracy of each node's estimate of the average at each time instant and the rate of dynamics. For our algorithm, we characterize this tradeoff and establish it to be near optimal. The dependence of the accuracy of the algorithm on the rate of dynamics as well as on the underlying graph structure is quantified.
Author: Huaqing Li
Publisher: Springer Nature
ISBN: 9811561095
Category : Technology & Engineering
Languages : en
Pages : 243
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Book Description
This book offers a valuable reference guide for researchers in distributed optimization and for senior undergraduate and graduate students alike. Focusing on the natures and functions of agents, communication networks and algorithms in the context of distributed optimization for networked control systems, this book introduces readers to the background of distributed optimization; recent developments in distributed algorithms for various types of underlying communication networks; the implementation of computation-efficient and communication-efficient strategies in the execution of distributed algorithms; and the frameworks of convergence analysis and performance evaluation. On this basis, the book then thoroughly studies 1) distributed constrained optimization and the random sleep scheme, from an agent perspective; 2) asynchronous broadcast-based algorithms, event-triggered communication, quantized communication, unbalanced directed networks, and time-varying networks, from a communication network perspective; and 3) accelerated algorithms and stochastic gradient algorithms, from an algorithm perspective. Finally, the applications of distributed optimization in large-scale statistical learning, wireless sensor networks, and for optimal energy management in smart grids are discussed.
Author: Angelia Nedić
Publisher: Springer
ISBN: 3319971425
Category : Business & Economics
Languages : en
Pages : 317
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Book Description
This book contains three well-written research tutorials that inform the graduate reader about the forefront of current research in multi-agent optimization. These tutorials cover topics that have not yet found their way in standard books and offer the reader the unique opportunity to be guided by major researchers in the respective fields. Multi-agent optimization, lying at the intersection of classical optimization, game theory, and variational inequality theory, is at the forefront of modern optimization and has recently undergone a dramatic development. It seems timely to provide an overview that describes in detail ongoing research and important trends. This book concentrates on Distributed Optimization over Networks; Differential Variational Inequalities; and Advanced Decomposition Algorithms for Multi-agent Systems. This book will appeal to both mathematicians and mathematically oriented engineers and will be the source of inspiration for PhD students and researchers.
Author: Christoforos N. Hadjicostis
Publisher: Foundations and Trends (R) in Systems and Control
ISBN: 9781680834383
Category : Automatic control
Languages : en
Pages : 208
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Book Description
The emergence of complex systems that are controlled over wireless and wired broadband networks, ranging from smart grids and traffic networks to embedded electronic devices and robotic networks, has sparked huge interest in distributed control problems. This is due to the need to properly coordinate the information exchange between sensors, actuators, and controllers in order to enforce a desirable behavior, without relying on a centralized decision maker. This monograph focuses on the key operations of distributed average consensus and weight/flow balancing under a variety of communication topologies and adversarial network conditions such as delays and packet drops. Divided into two parts, Theory and Applications, it first provides the reader with thorough grounding into the theory underpinning the research before discussing two applications in detail. Namely, the coordination of distributed energy resources and the computation of PageRank values. The monograph will be of interest to all researchers, students and practitioners working control, coordination, and optimization tasks in many emerging networked applications.
Author: Giuseppe Notarstefano
Publisher:
ISBN: 9781680836189
Category : Technology & Engineering
Languages : en
Pages : 148
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Book Description
In an increasingly connected world, the term cyber-physical networks has been coined to refer to the communication among devices that is turning smart devices into smart (cooperating) systems. The distinctive feature of such systems is that significant advantage can be obtained if its interconnected, complex nature is exploited. Several challenges arising in cyber-physical networks can be stated as optimization problems. Examples are estimation, decision, learning and control applications. In cyber-physical networks, the goal is to design algorithms, based on the exchange of information among the processors, that take advantage of the aggregated computational power. Distributed Optimization for Smart Cyber-Physical Networks provides a comprehensive overview of the most common approaches used to design distributed optimization algorithms, together with the theoretical analysis of the main schemes in their basic version. It identifies and formalizes classes of problem set-ups that arise in motivating application scenarios. For each set-up, in order to give the main tools for analysis, tailored distributed algorithms in simplified cases are reviewed. Extensions and generalizations of the basic schemes are also discussed at the end of each chapter. Distributed Optimization for Smart Cyber-Physical Networks provides the reader with an accessible overview of the current research and gives important pointers towards new developments. It is an excellent starting point for research and students unfamiliar with the topic.
Author: Alberto Bemporad
Publisher: Springer Science & Business Media
ISBN: 0857290320
Category : Mathematics
Languages : en
Pages : 373
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Book Description
This book nds its origin in the WIDE PhD School on Networked Control Systems, which we organized in July 2009 in Siena, Italy. Having gathered experts on all the aspects of networked control systems, it was a small step to go from the summer school to the book, certainly given the enthusiasm of the lecturers at the school. We felt that a book collecting overviewson the important developmentsand open pr- lems in the eld of networked control systems could stimulate and support future research in this appealing area. Given the tremendouscurrentinterests in distributed control exploiting wired and wireless communication networks, the time seemed to be right for the book that lies now in front of you. The goal of the book is to set out the core techniques and tools that are ava- able for the modeling, analysis and design of networked control systems. Roughly speaking, the book consists of three parts. The rst part presents architectures for distributed control systems and models of wired and wireless communication n- works. In particular, in the rst chapter important technological and architectural aspects on distributed control systems are discussed. The second chapter provides insight in the behavior of communication channels in terms of delays, packet loss and information constraints leading to suitable modeling paradigms for commu- cation networks.
