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Discrete Networked Dynamic Systems: Analysis and Performance provides a high-level treatment of a general class of linear discrete-time dynamic systems interconnected over an information network, exchanging relative state measurements or output measurements. It presents a systematic analysis of the material and provides an account to the math development in a unified way. The topics in this book are structured along four dimensions: Agent, Environment, Interaction, and Organization, while keeping global (system-centered) and local (agent-centered) viewpoints. The focus is on the wide-sense consensus problem in discrete networked dynamic systems. The authors rely heavily on algebraic graph theory and topology to derive their results. It is known that graphs play an important role in the analysis of interactions between multiagent/distributed systems. Graph-theoretic analysis provides insight into how topological interactions play a role in achieving coordination among agents. Numerous types of graphs exist in the literature, depending on the edge set of G. A simple graph has no self-loop or edges. Complete graphs are simple graphs with an edge connecting any pair of vertices. The vertex set in a bipartite graph can be partitioned into disjoint non-empty vertex sets, whereby there is an edge connecting every vertex in one set to every vertex in the other set. Random graphs have fixed vertex sets, but the edge set exhibits stochastic behavior modeled by probability functions. Much of the studies in coordination control are based on deterministic/fixed graphs, switching graphs, and random graphs. This book addresses advanced analytical tools for characterization control, estimation and design of networked dynamic systems over fixed, probabilistic and time-varying graphs Provides coherent results on adopting a set-theoretic framework for critically examining problems of the analysis, performance and design of discrete distributed systems over graphs Deals with both homogeneous and heterogeneous systems to guarantee the generality of design results
Discrete-event dynamic systems (DEDs) permeate our world. They are of great importance in modern manufacturing processes, transportation and various forms of computer and communications networking. This book begins with the mathematical basics required for the study of DEDs and moves on to present various tools used in their modeling and control. Industrial examples illustrate the concepts and methods discussed, making this book an invaluable aid for students embarking on further courses in control, manufacturing engineering or computer studies.
The book gives an introduction to networked control systems and describes new modeling paradigms, analysis methods for event-driven, digitally networked systems, and design methods for distributed estimation and control. Networked model predictive control is developed as a means to tolerate time delays and packet loss brought about by the communication network. In event-based control the traditional periodic sampling is replaced by state-dependent triggering schemes. Novel methods for multi-agent systems ensure complete or clustered synchrony of agents with identical or with individual dynamics. The book includes numerous references to the most recent literature. Many methods are illustrated by numerical examples or experimental results.
This book provides an introduction to discrete dynamical systems – a framework of analysis that is commonly used in the ?elds of biology, demography, ecology, economics, engineering, ?nance, and physics. The book characterizes the fundamental factors that govern the quantitative and qualitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for those systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors that govern the evolution of state variables in the elementary context of one-dimensional, ?rst-order, linear, autonomous systems. The f- damental insights about the forces that a?ect the evolution of these - ementary systems are subsequently generalized, and the determinants of the trajectories of multi-dimensional, nonlinear, higher-order, non- 1 autonomous dynamical systems are established. Chapter 1 focuses on the analysis of the evolution of state variables in one-dimensional, ?rst-order, autonomous systems. It introduces a method of solution for these systems, and it characterizes the traj- tory of a state variable, in relation to a steady-state equilibrium of the system, examining the local and global (asymptotic) stability of this steady-state equilibrium. The ?rst part of the chapter characterizes the factors that determine the existence, uniqueness and stability of a steady-state equilibrium in the elementary context of one-dimensional, ?rst-order, linear autonomous systems.
This monograph provides a comprehensive exploration of new tools for modelling, analysis, and control of networked dynamical systems. Expanding on the authors’ previous work, this volume highlights how local exchange of information and cooperation among neighboring agents can lead to emergent global behaviors in a given networked dynamical system. Divided into four sections, the first part of the book begins with some preliminaries and the general networked dynamical model that is used throughout the rest of the book. The second part focuses on synchronization of networked dynamical systems, synchronization with non-expansive dynamics, periodic solutions of networked dynamical systems, and modulus consensus of cooperative-antagonistic networks. In the third section, the authors solve control problems with input constraint, large delays, and heterogeneous dynamics. The final section of the book is devoted to applications, studying control problems of spacecraft formation flying, multi-robot rendezvous, and energy resource coordination of power networks. Modelling, Analysis, and Control of Networked Dynamical Systems will appeal to researchers and graduate students interested in control theory and its applications, particularly those working in networked control systems, multi-agent systems, and cyber-physical systems. This volume can also be used in advanced undergraduate and graduate courses on networked control systems and multi-agent systems.
A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.
This text presents a unique treatment of network control systems. Drawing from fundamental principles of dynamical systems theory and dynamical thermodynamics, the authors develop a continuous-time, discrete-time, and hybrid dynamical system and control framework for linear and nonlinear large-scale network systems. The proposed framework extends the concepts of energy, entropy, and temperature to undirected and directed information networks. Continuous-time, discrete-time, and hybrid thermodynamic principles are used to design distributed control protocol algorithms for static and dynamic networked systems in the face of system uncertainty, exogenous disturbances, imperfect system network communication, and time delays. Network Information Systems: A Dynamical Systems Approach is written for applied mathematicians, dynamical systems theorists, control theorists, and engineers. Researchers and graduate students in a variety of fields who seek a fundamental understanding of the rich behavior of controlled large-scale network systems will also find this book useful. This book can be used for a first course on control design of large-scale network systems, such as control protocols for network systems, network information systems, a dynamical systems approach to network systems, and network thermodynamic systems. The prerequisites are a first course in nonlinear systems theory and a first course in advanced (multivariable) calculus.
This book introduces the principle theories and applications of control and filtering problems to address emerging hot topics in feedback systems. With the development of IT technology at the core of the 4th industrial revolution, dynamic systems are becoming more sophisticated, networked, and advanced to achieve even better performance. However, this evolutionary advance in dynamic systems also leads to unavoidable constraints. In particular, such elements in control systems involve uncertainties, communication/transmission delays, external noise, sensor faults and failures, data packet dropouts, sampling and quantization errors, and switching phenomena, which have serious effects on the system’s stability and performance. This book discusses how to deal with such constraints to guarantee the system’s design objectives, focusing on real-world dynamical systems such as Markovian jump systems, networked control systems, neural networks, and complex networks, which have recently excited considerable attention. It also provides a number of practical examples to show the applicability of the presented methods and techniques. This book is of interest to graduate students, researchers and professors, as well as R&D engineers involved in control theory and applications looking to analyze dynamical systems with constraints and to synthesize various types of corresponding controllers and filters for optimal performance of feedback systems.
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.
Discrete-event dynamic systems (DEDs) permeate our world. They are of great importance in modern manufacturing processes, transportation and various forms of computer and communications networking. This book begins with the mathematical basics required for the study of DEDs and moves on to present various tools used in their modeling and control. Industrial examples illustrate the concepts and methods discussed, making this book an invaluable aid for students embarking on further courses in control, manufacturing engineering or computer studies.