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SPRINGER BRIEFS IN ELECTRICAL AND COMPUTER ENGINEERING  CONTROL, AUTOMATION AND ROBOTICS Minghui Zhu Sonia Martínez Distributed Optimization-Based Control of Multi- Agent Networks in Complex Environments 123

SpringerBriefs in Electrical and Computer Engineering Control, Automation and Robotics Series editors Tamer Başar Antonio Bicchi Miroslav Krstic

More information about this series at http://www.springer.com/series/10198

Minghui Zhu Sonia Martínez Distributed Optimization-Based Control of Multi-Agent Networks in Complex Environments 123

Minghui Zhu Department of Electrical Engineering Pennsylvania State University University Park, PA USA Sonia Martínez Department of Mechanical and Aerospace Engineering University of California, San Diego La Jolla, CA USA ISSN 2191-8120 ISSN 2191-8112 SpringerBriefs in Electrical and Computer Engineering ISSN 2192-6786 ISSN 2192-6794 SpringerBriefs in Control, Automation and Robotics ISBN 978-3-319-19071-6 DOI 10.1007/978-3-319-19072-3 (electronic) (electronic) ISBN 978-3-319-19072-3 (eBook) Library of Congress Control Number: 2015939436 Mathematics Subject Classiﬁcation: 93-02 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microﬁlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, in this publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. trademarks, service marks, etc. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)

To Danying and my parents Minghui Zhu To Jorge, Jon Nicolás, and Alexandra Sonia Martínez

Preface Smart communication, computing, sensing, and actuation devices are increasingly permeating through our world in an unstoppable manner. These technological advances are fostering the emergence of a variety of large-scale networked systems and applications, including multivehicle networks, the smart grid, smart buildings, medical device networks, intelligent transportation systems, and social networks. It has been an efﬁcient practice to abstract these complex systems as multi-agent networks. In particular, each agent in the network represents a strategic entity and is able to communicate, sense, compute, and autonomously react to surrounding changes. The interactions among the agents allow them to solve problems beyond their individual capabilities, resulting in a whole that is certainly more than the sum of its parts. In order to ensure that the network performs at an optimal level, agents face the problem of choosing the best option among a set of candidates. Distributed opti- mization-based control (DOC, for short) provides a holistic and mathematically rigorous framework to entail network-wide optimal decision making and control. In particular, desired network-wide behavior is encoded as a DOC problem where agents seek for different subobjectives and are required to obey inhomogeneous constraints of physical dynamics and decision choices. This class of problems is characterized by a number of salient features. First, the network consists of a large number of geographically distributed agents. Second, due to information privacy, the agents may not be willing to disclose their own components which deﬁne the DOC problem. Third, the agents are expected to self-adapt to internal faults and external changes. Given these features, the top-down frameworks in classic cen- tralized and hierarchical approaches are not well suited for the needs of DOC. It necessitates bottom-up paradigms, i.e, the synthesis of distributed algorithms which allow the agents to coordinate with others via autonomous actions and local interactions resulting into an emerging network-wide behavior that globally opti- mizes the problem of interest. Bottom-up paradigms are characterized by that the desired global behavior emerges from local actions and interactions. In a number of engineering applications, agents are required to operate in dynamically changing, uncertain, and hostile environments. Take multivehicle vii

viii Preface networks as an example. Due to a limited communication bandwidth, underwater vehicles can only exchange information intermittently and thus intervehicle communication topologies frequently change over time. Ground vehicles may be commanded to perform surveillance missions in a region where the environmental information is not provided in advance. In addition, aerial vehicles operate far away from base stations and thus can be compromised by human adversaries who may attack the cyber infrastructures. In order to ensure the high performance and high conﬁdence of multi-agent networks, DOC should explicitly take into account the unforeseeable elements during the algorithm design and performance analysis. An Outline of the Book This book aims at a concise and in-depth exposition of speciﬁc algorithmic solu- tions for DOC and their performance analysis. We focus on addressing the par- ticular challenges topological dynamics, environmental uncertainties, and cyber adversaries via integrating mis- cellaneous ideas and tools from Dynamic Systems, Control Theory, Graph Theory, Optimization, Game Theory, and Markov Chains. To achieve this goal, we organize the book in the following way: induced by the environmental complexities: Chapter 1 presents a summary of mathematical tools for DOC used in this book. We start with the consensus problem, a canonical problem in multi-agent networks. In particular, we introduce the matrix representation of multi-agent networks as well as the algorithms and convergence results for static and dynamic average consen- sus. After this, we present a concise introduction to convex optimization and noncooperative game theory. We conclude with a treatment of Markov chains and stochastic stability. Chapter 2 studies a class of generic distributed convex optimization problems. In particular, each agent is associated with a private objective function and a private convex constraint set. Meanwhile, all the agents are subject to a pair of global inequality and equality constraints. The key feature of the problem is that all the component functions depend upon a global decision variable. The agents aim to agree upon two global quantities: (1) a global minimizer of the sum of all private objective functions, simultaneously enforcing all the given constraints; (2) the induced optimal value. Chapter 3 investigates a game theoretic solution of an optimal sensor deploy- ment problem. In particular, a set of mobile visual sensors are self-deployed in a geographically extended environment to accomplish a variety of Intelligence, Surveillance and Reconnaissance (ISR) missions, such as environmental monitor- ing, source seeking, and target assignment. The key feature of the problem is that the environmental distribution function is unknown a priori but its values can be measured on site. Chapter 4 considers attack-resilient distributed formation control of operator- vehicle networks. Through communication infrastructures, human operators

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