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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A detailed and systematic introduction to the distributed cooperative control of multi-agent systems from a theoretical, network perspective * Features detailed analysis and discussions on the distributed cooperative control and dynamics of multi-agent systems * Covers comprehensively first order, second order and higher order systems, swarming and flocking behaviors * Provides a broad theoretical framework for understanding the fundamentals of distributed cooperative control
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Seitenzahl: 307
Veröffentlichungsjahr: 2016
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Table of Contents
Cover
Title Page
Copyright
Preface
Chapter 1: Introduction
1.1 Background
1.2 Organization
Chapter 2: Consensus in Multi-agent Systems
2.1 Consensus in Linear Multi-agent Systems
2.2 Consensus in Nonlinear Multi-agent Systems
2.3 Notes
Chapter 3: Second-Order Consensus in Multi-agent Systems
3.1 Second-Order Consensus in Linear Multi-agent Systems
3.2 Second-Order Consensus in Nonlinear Multi-agent Systems
3.3 Notes
Chapter 4: Higher-Order Consensus in Multi-agent Systems
4.1 Preliminaries
4.2 Higher-Order Consensus in a General Form
4.3 Leader-Follower Control in Multi-agent Systems
4.4 Simulation Examples
4.5 Notes
Chapter 5: Stability Analysis of Swarming Behaviors
5.1 Preliminaries
5.2 Analysis of Swarm Cohesion
5.3 Swarm Cohesion in a Noisy Environment
5.4 Cohesion in Swarms with Switched Topologies
5.5 Cohesion in Swarms with Changing Topologies
5.6 Simulation Examples
5.7 Notes
Chapter 6: Distributed Leader-Follower Flocking Control
6.1 Preliminaries
6.2 Distributed Leader-Follower Control with Pinning Observers
6.3 Simulation Examples
6.4 Notes
Chapter 7: Consensus of Multi-agent Systems with Sampled Data Information
7.1 Problem Statement
7.2 Second-Order Consensus of Multi-agent Systems with Sampled Full Information
7.3 Second-Order Consensus of Multi-agent Systems with Sampled Position Information
7.4 Consensus of Multi-agent Systems with Nonlinear Dynamics and Sampled Information
7.5 Notes
Chapter 8: Consensus of Second-Order Multi-agent Systems with Intermittent Communication
8.1 Problem Statement
8.2 The Case with a Strongly Connected Topology
8.3 The Case with a Topology Having a Directed Spanning Tree
8.4 Consensus of Second-Order Multi-agent Systems with Nonlinear Dynamics and Intermittent Communication
8.5 Notes
Chapter 9: Distributed Adaptive Control of Multi-agent Systems
9.1 Distributed Adaptive Control in Complex Networks
9.2 Distributed Control Gains Design for Second-Order Consensus in Nonlinear Multi-agent Systems
9.3 Notes
Chapter 10: Distributed Consensus Filtering in Sensor Networks
10.1 Preliminaries
10.2 Distributed Consensus Filters Design for Sensor Networks with Fully-Pinned Controllers
10.3 Distributed Consensus Filters Design for Sensor Networks with Pinning Controllers
10.4 Distributed Consensus Filters Design for Sensor Networks with Pinning Observers
10.5 Simulation Examples
10.6 Notes
Chapter 11: Delay-Induced Consensus and Quasi-Consensus in Multi-agent Systems
11.1 Problem Statement
11.2 Delay-Induced Consensus and Quasi-Consensus in Multi-agent Dynamical Systems
11.3 Motivation for Quasi-Consensus Analysis
11.4 Simulation Examples
11.5 Notes
Chapter 12: Conclusions and Future Work
12.1 Conclusions
12.2 Future Work
Bibliography
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
Distributed Cooperative Control of Multi-Agent Systems
Wenwu Yu
Southeast University, China
Guanghui Wen
Southeast University, China
Guanrong Chen
City University of Hong Kong, China
Jinde Cao
Southeast University, China
This edition first published 2016
© 2016 Higher Education Press. All rights reserved.
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Library of Congress Cataloging-in-Publication Data
Names: Yu, Wenwu, 1982-
Title: Distributed cooperative control of multi-agent systems / Wenwu Yu [and four others].
Description: Singapore : John Wiley & Sons, Inc., [2016] | Includes bibliographical references and index.
Identifiers: LCCN 2016018240 (print) | LCCN 2016023245 (ebook) | ISBN 9781119246206 (cloth) | ISBN 9781119246237 (pdf) | ISBN 9781119246220 (epub)
Subjects: LCSH: Chaotic synchronization. | Synchronization. | System analysis.
Classification: LCC Q172.5.S96 D57 2017 (print) | LCC Q172.5.S96 (ebook) | DDC 003/.7-dc23
LC record available at https://lccn.loc.gov/2016018240
Preface
In the natural, social and technological worlds, there are many large-scale complex networks with multiple agents for which centralized control is often difficult or even impossible to apply. Therefore, distributed cooperative control of multi-agent systems has been widely investigated for its easy implementation, strong robustness, and high self-organizability. In a multi-agent system under a network communication structure, to cooperative with other agents, everyone needs to share information with its adjacent peers so that all agents can agree on a common goal of interest. Recently, some progress has been made in analyzing collective behaviors in such dynamical networks for which closely related focal topics are synchronization, consensus, swarming and flocking. However, there are very few books focusing on distributed cooperative control of multi-agent systems addressing a broad spectrum of scientific interest. It is now clear that the impact of cooperative control of multiple autonomous agents in engineering and technology is prominent and will be far-reaching. Thus, an in-depth study with detailed analysis of this subject will benefit both theoretical research and engineering applications in the near-future development of related technologies.
The authors of this book have been working together on distributed cooperative control of multi-agent systems for about seven years with some relatively comprehensive results developed on the topic. This book summaries their main contributions in the field with general background knowledge and information, for a broad discipline, including particularly dynamics of general multi-agent systems, for example first-order, second-order and higher-order consensus, as well as swarming and flocking behaviors. Some technical issues about multi-agent systems with sampled data information transmission, missing control input, adaptive control and filters design are also investigated.
This book presents the basic knowledge along with a thorough review of the-state-of-the-art progress in the field. The contents of the book are summarized as follows: (1) first-order, second-order, and higher-order consensus are discussed for both linear and nonlinear multi-agent systems in Chapters 2–4; (2) stability analysis of a general swarming model with hybrid nonlinear profiles, stochastic noise, and switching topologies is investigated in Chapter 5; (3) distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities is studied in Chapter 6; (4) hybrid control of multi-agent systems including sampled-data control and intermittent control is further discussed in Chapters 7 and 8; (5) fully adaptive control protocols for multi-agent systems are designed in Chapter 9; (6) some applications to distributed consensus filtering in sensor networks are presented in ChGapter 10; (7) an interesting problem for delay-induced consensus in multi-agent systems with second-order dynamics is addressed in Chapter 11; (8) conclusions are drawn with future research outlook in Chapter 12.
This work is supported by the National Natural Science Foundation of China under Grant Nos. 61322302, 61304168, and by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20130595. The first author, Wenwu Yu, would like to express his deepest gratitude to his wife Lingling Yao and little daughter, Zhiyao Yu for their love and unconditional support; this academic book a good gift for them.
Wenwu Yu, Guanghui Wen, Guanrong Chen, and Jinde CaoWinter, 2015
Chapter 1Introduction
1.1 Background
1.1.1 Networked Multi-agent Systems
Most large-scale systems in nature and human societies, such as biological neural networks, ecosystems, metabolic pathways, the Internet, the WWW, and electrical power grids can be described by networks with nodes representing individuals in the system and edges representing the connections between them. Recently, the study of various complex networks and systems has attracted increasing attention from researchers in various fields of physics, mathematics, engineering, biology, and sociology alike [8, 35, 62, 90, 117–119, 123, 142].
In the early 1960s, Erdös and Rényi (ER) proposed a random-graph model, which laid a solid foundation for modern network theory [35]. In a random network, each pair of nodes is connected with a certain probability. In order to describe a transition from a regular network to a random network, Watts and Strogatz (WS) proposed an interesting small-world network model [123]. Then, Newman and Watts (NW) modified the original WS model to generate another version of the small-world model [80]. Meanwhile, Barabási and Albert (BA) proposed a scale-free network model, in which the degree distribution of the nodes follows a power-law form [8]. Since then, small-world and scale-free networks have been extensively investigated worldwide.
Cooperative and collective behaviors in networks of multiple autonomous agents have also received considerable attention in recent years due to the growing interest in understanding the amazing animal group behaviors, such as flocking and swarming, and also due to their emerging broad applications in sensor networks, UAV (unmanned air vehicles) formations, and robotic teams. To coordinate with other agents in a network, every agent needs to share information with its adjacent peers so that all can agree on a common goal of interest, such as the value of some measurement in a sensor network, the heading in a UAV formation, or the target position of a robotic team.
Recently, some progress has been made in analyzing cooperative control for collective behaviors in dynamical multi-agent systems, for which some closely related focal topics are synchronization [90, 117, 118, 142], consensus [15, 57, 77, 81, 98, 99, 101, 115], swarming [44, 45], and flocking [82]. More details can be found in survey papers [4, 17, 84, 120].
1.1.2 Collective Behaviors and Cooperative Control in Multi-agent Systems
Synchronization is a typical collective behavior in nature. Since the pioneering work of Pecora and Carroll [90], chaos control and synchronization have received a great deal of attention due to their potential applications in secure communications, chemical reactions, biological systems, and so on [143, 145]. Typically, there are large numbers of nodes in real-world complex networks. In recent years, a lot of work has been devoted to the study of synchronization in various large-scale complex networks [14, 70, 117, 118, 142]. In [117, 118], local synchronization was investigated by the transverse stability to the synchronization manifold, where synchronization was discussed on small-world and scale-free networks. In [132, 134], a distance from the collective states to the synchronization manifold was defined, and based on this, some results were obtained for global synchronization of coupled systems [14, 70]. A general criterion was derived in [142], where the network sizes can be extended to be much larger than those given in [14, 70]. However, it is still very difficult to ensure global synchronization in general large-scale networks due to the computational complexity. Recently, global pinning synchronization for a class of complex networks with switched topologies was addressed in [130] by using tools from stability analysis of switched systems.
The consensus problem has a long history in the field of computer science especially for distributed computing [74]. The idea of consensus was originated from statistical consensus theory by DeGroot [28], which was revisited two decades later for pattern recognition using multi-sensors [10]. Usually, it refers to the problem of how to reach agreement among a group of autonomous agents in a dynamically changing environment [99]. One of the main challenges in solving such a consensus problem is that an agreement has to be reached by all agents in the whole dynamic network while the information of each agent is shared only locally. Various models have been used to study the consensus problem. Vicsek et al. studied a discrete-time system that models a group of autonomous agents moving in the plane with the same speed but different headings [115]. It was shown, through simulation, that using a distributed averaging rule, agents could eventually move in the same direction without centralized coordination. Vicsek's model by nature is a simplified version of the model proposed earlier by Reynolds [101]. Analysis on Vicsek's model, or its continuous-time version, shows that the connectivity of the time-varying graph that describes the neighboring relationships within the group is key in achieving consensus [15, 57, 81, 77, 98]. In particular, in [81], Olfati-Saber and Murray established the relationship between the algebraic connectivity (also called the Fiedler eigenvalue [37]) and the speed of convergence when the underlying directed graph is balanced. A broader class of directed graphs that may lead to reaching consensus are those that contain spanning trees [98], which are also called rooted graphs [15].
It is interesting to observe that Vicsek's model is similar to a class of models discussed in synchronization of complex networks [14, 70, 117, 118, 134, 142]. In 1998, Pecora and Carroll made use of a master stability function to study the synchronization of coupled complex networks [90]. To date, stability and synchronization of small-world and scale-free networks have been investigated extensively using this master stability function method.
In the literature, most work on the consensus problem considered the case where agents are governed by first-order dynamics [11, 57, 72, 81, 98, 114, 134, 141, 142, 151]. Meanwhile, there is a growing interest in consensus algorithms where all agents are governed by second-order dynamics [50, 51, 82, 93, 95, 97, 146]. More precisely, second-order consensus refers to the problem of reaching an agreement among a group of autonomous agents governed by second-order dynamics. A detailed analysis of second-order consensus algorithms is a key step to bring more realistic dynamics into the model of each individual agent based on the general framework of multi-agent systems, thus it can help control engineers to implement distributed cooperative control strategies for networked multi-agent systems. It has been shown that, in sharp contrast to the first-order consensus problem, consensus may fail to be achieved for agents with second-order dynamics even if the network topology has a directed spanning tree [97].
On the other hand, time delay is ubiquitous in biological, physical, chemical, and electrical systems [11, 114]. In biological and communication networks, time delays are usually inevitable due to the possibly slow process of interactions among agents. It has been observed from numerical experiments that consensus algorithms without considering time delays may lead to unexpected instability. In [11, 114], some sufficient conditions were derived for first-order consensus in delayed multi-agent systems.
Very recently, some higher-order consensus algorithms in cooperative control of multi-agent systems were studied, such as in [100] based on the results derived in [97]. However, only third-order consensus was discussed in detail therein. In this book, a general higher-order consensus protocol is designed and analyzed based on the transverse stability to the consensus manifold, which originates from the study of synchronization in complex networks [117]. A detailed analysis of the higher-order consensus algorithms is a prerequisite to introducing more realistic dynamics into the model of each individual agent.
As validated by biological field studies and engineering robotic experiments, swarm cohesion can be achieved in a distributed fashion despite the fact that each agent may only have local information about its nearest neighbors. An in-depth understanding of the principles behind swarming behaviors will help engineers to develop distributed cooperative control strategies and algorithms for networked dynamical systems, such as formations of UAVs, autonomous robotic teams, and mobile sensors networks. Synchronous distributed coordination rules for swarming groups in one- or two-dimensional spaces were studied in [58], where convergence and stability analysis were given. In [44, 45], stability properties of a continuous-time model for swarm aggregation in the -dimensional space was discussed, and an asymptotic bound for the spatial size of the swarm was computed using the parameters of the swarm model.
In [101], three heuristic rules were suggested by Reynolds to animate flocking behavior: (1) velocity consensus, (2) center cohesion, and (3) collision avoidance. In order to embody the three Reynolds' rules, Tanner et al. designed flocking algorithms in [110, 111], where a collective potential function and a velocity consensus term were introduced. Later, in [82], Olfati-Saber proposed a general framework to investigate distributed flocking algorithms where, in particular, three algorithms were developed for free and constrained flocking. In [110, 111], it was pointed out that due to the time-varying network topology, the set of differential equations describing the flocking behavior of a multi-agent dynamical system is in general nonsmooth; therefore, several techniques from nonsmooth analysis, such as Filippov solutions [38], generalized gradient [25], and differential inclusion [87], were applied for analysis.
1.1.3 Network Control in Multi-agent Systems
In the case where the whole network cannot synchronize by itself, some controllers may be designed and applied to force the network to synchronize. However, it is literally impossible to add controllers to all nodes. To reduce the number of controlled nodes, some local feedback injections may be applied only to a fraction of network nodes, which is known as pinning control [23, 119, 151]. In [47], pinning control of spatiotemporal chaos, and later in [89], global and local control of spatiotemporal chaos in coupled map lattices, were discussed. Recently, in [119], both specific and random pinning schemes were studied, where specific pinning to the nodes with large degrees is shown to require a smaller number of controlled nodes than the random pinning scheme, but the former requires more information about the network than the latter.
Recently, hybrid systems, namely complex systems with both continuous-time and discrete-time event dynamics, have been extensively investigated in the literature, for example continuous-time systems with impulsive responses, sampled data, quantization, to name just a few. Some real-world applications can be modeled by continuous-time systems together with some discrete-time events, such as an A/C unit containing some discrete modes with on or off states, changing the temperature continuously over time. In practice, it is quite difficult to measure the continuous information transmission due to the unreliability of information channels, the capability of transmission bandwidths of networks, etc. Thus, it is more practical to apply sampled-data control, which has been widely studied recently and applied in many real-world systems such as radar tracking systems, power grids, and temperature control. It has been found that sampled-data control has many good properties such as robustness and low cost. Recently, many results have been established from investigating the second-order consensus in multi-agent systems with sampled data. For example, some conditions were derived for multi-agent systems with sampled control by using zero-order holds or direct discretization [18, 41, 66, 163]. On the other hand, consensus of continuous-time multi-agent systems with time-varying topologies and sampled-data control was discussed in [42], and communication delays were considered in multi-agent systems with sampled-data control in [43, 162].
It should be noted that most of the results on consensus problems in multi-agent systems are derived based on a common assumption that the information is transmitted continuously among the agents, that is, each agent shares information with its neighbors without any communication constraints. However, this may not be the case in reality. In some cases, the mobile agents can only communicate with their neighbors at some disconnected time intervals. In order to describe such multi-agent systems more appropriately, a second-order consensus protocol based on globally synchronous intermittent local information feedback was proposed in [124, 129, 126] to guarantee the states of agents converging to consensus asymptotically.
In the literature, many derived conditions for ensuring network synchronization were only sufficient but not necessary, thus are somewhat conservative. Lately, a lot of work has been devoted to using adaptive strategies to adjust network parameters so as to derive better conditions for reaching network synchronization, which employed some existing results from adaptive synchronization in nonlinear systems [139, 155]. For example, in [23, 151, 165, 166], adaptive laws were applied to the control gains from the leader to the followers, and in [23, 151] centralized adaptive schemes were designed on the network coupling strengths. However, there is not much work on how to update the coupling weights of the network for reaching synchronization. In addition, in order to reach consensus or synchronization, some additional global conditions in terms of the spectrum of the Laplacian matrix or its eigenvalues must be satisfied even if the multi-agent system is linear, which actually did not take full advantage of the powerful distributed protocol technology. For example, in [50, 95, 146, 149], in order to reach second-order consensus, the Laplacian matrix or its eigenvalues must be known a priori. To overcome the disadvantage for checking the global information under the local distributed protocol, fully distributed adaptive control in multi-agent systems was investigated recently, which will be introduced in this book.
1.1.4 Distributed Consensus Filtering in Sensor Networks
Sensor networks have attracted increasing attention due to their wide applications in robotics, surveillance and environment monitoring, information collection, wireless communication networks, and so on. A sensor network consists of a large number of sensor nodes distributing over a spatial region. Each sensor has some levels of communication, intelligence for signal processing, and data fusion, which build up a sensing network. Due to the limited energy, computational ability, and communication capability, typically a large number of sensor nodes are used in a wider region so as to achieve higher accuracy of estimating the quantities of interest. Each sensor node is equipped with a microelectronic device having limited power source, which might not be able to transmit messages over a large sensor network. In order to save energy, a natural way is to carry out data fusion to reduce the communication overhead. Therefore, distributed estimation and tracking is one of the most important problems in large-scale sensor networks today. From a network-theoretic perspective, a large-scale sensor network can be viewed as a complex network or a multi-agent system with each node representing a sensor and each edge carrying the information exchange between two sensors. It would be interesting to see how synchronization of complex networks [70, 117, 118, 142] and consensus of multi-agent systems [57, 81, 98] can be used in distributed consensus filtering design. In a complex network, each node communicates with its neighboring nodes to exchange information, so that all the states could finally reach the synchronization or consensus manifold. Therefore, it is quite natural to use the synchronization fundamentals of complex networks and consensus in multi-agent systems as the theoretic basis for distributed consensus filtering design. Practically, it is very difficult to observe all the states of the target, so pinning observers may be designed in the case where the informed sensors can only measure partial states of the target. This notion will also be introduced in the present book.
1.2 Organization
This book focuses on distributed cooperative control in multi-agent systems, which includes complex dynamics, hybrid control, adaptive control, distributed filtering, etc. The contents of the book are summarized as follows.
In Chapter 2, first-order consensus for cooperative agents with nonlinear dynamics in a directed network is discussed. Both local and global consensus are defined and investigated. Techniques for studying synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus. The local consensus problem is first studied by combining tools of complex analysis, local consensus manifold approach, and Lyapunov methods. A generalized algebraic connectivity is then derived for studying the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees, for which ideas from algebraic graph theory, matrix theory, and Lyapunov methods are utilized. The concept of a virtual network, which has the same spectrum as the original one, is formulated to simplify the analysis.
In Chapter 3, some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems are presented. Here, theoretical analysis is carried out for the case where each agent with second-order dynamics is governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system with communication delays. A necessary and sufficient condition is established, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Then, the second-order consensus problem is extended to multi-agent systems with nonlinear dynamics and directed topologies where the final asymptotic velocity is time-varying. Some sufficient conditions are derived for reaching second-order consensus in multi-agent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and the Lyapunov control approach.
Next, some general higher-order distributed consensus protocols in multi-agent dynamical systems are designed in Chapter 4. The notion of network synchronization is first introduced, with some necessary and sufficient conditions derived for higher-order consensus. It is found that consensus can be reached if and only if all subsystems are asymptotically stable. Based on this result, consensus regions are characterized. It is proved that for the th-order consensus, there are at most disconnected stable and unstable consensus regions. It is shown that consensus can be achieved if and only if all the nonzero eigenvalues of the Laplacian matrix lie in the stable consensus regions. Moreover, since the ratio of the largest to the smallest nonzero eigenvalues of the Laplacian matrix plays a key role in reaching consensus, a scheme for choosing the coupling strength is derived, which determines the eigen-ratio. Furthermore, a leader-follower control problem with full-state or partial-state observations in multi-agent dynamical systems is considered respectively, which reveals that the agents with very small degrees must be informed.
In Chapter 5, the stability of a continuous-time swarm model with nonlinear profiles is investigated. It is shown that, under some mild conditions, all agents in a swarm can reach cohesion within a finite time, where some upper bounds for the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by allowing stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with changing communication topologies and unbounded repulsive interactions among agents are studied by nonsmooth analysis, where the sensing range of each agent is limited and the possibility of collision among nearby agents can be high.
In Chapter 6, using tools from algebraic graph theory and nonsmooth analysis in combination with the ideas of collective potential functions, velocity consensus and navigation feedback, a distributed leader-follower flocking algorithm for multi-agent dynamical systems with time-varying velocities is developed, where each agent is governed by second-order dynamics. The distributed leader-follower flocking algorithm deals with the case where the group has one virtual leader with time-varying velocity. For each agent, this algorithm consists of four terms: the first term is the self nonlinear dynamics, which
