Discrete-Time Control Systems

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which unifies across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and

Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.

This collection of essays was the first relatively comprehensive survey of the environmental history of China. Written by some of the world's leading Western and Chinese experts, Sediments of Time crystallises a new and distinct field of scholarship that studies what happens when human social systems interact with the rest of the natural world. This book shows how deforestation, land-reclamation, settlement, and water-control, when mixed with an ever-changing climate, shape a distinct and often precarious environment. Pioneering essays explore new methodologies of historical environmental research, comparative perspectives setting China in the context of the West and Japan, and the impact of the early modern ecological transformation on the spread of diseases such as cholera and tuberculosis. This is an indispensable book for anyone who wants to understand either the foundations of modern China, or the deeper origins of many of China's most daunting contemporary challenges.

This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the

Control systems design methodologies have long suffered the traditional and myopic dichotomy between time and frequency domain approaches, each of them being specialized to cope with only scarcely ove

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

A text for a graduate course on linear system theory, with core material on the theory of time-varying linear systems in both continuous- and discrete-time and the time-invariant case. Chapters on sub

Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engin

This compelling book, first published in 1996, is an exploration of the imaginary of perceptual control technologies at the beginning of the twenty-first century. William Bogard constructs a 'social science fiction' of how the revolution in simulation technology reconfigures and intensifies the role of surveillance in war, work, sexuality and private life, enabling forms of control which hyper realise our experience of time, space, agency and society itself. His is a critique of the imaginary in which control breaks free of its prior limits, an imaginary of unmediated perception with effects everywhere in fantastic systems for the relentless conversion of objects, events and people into information.

Provides unified coverage of the principles and methods of various disciplines' approaches to prediction and control of processes expressed by discrete-time models, especially adaptive prediction, for

In recent years significant progress has been made in the analysis and design of discrete-data and digital control systems. These systems have gained popularity and importance in industry due in part

Using a systems perspective, this updated version concentrates on the planning, scheduling and control factors of a project needed to bring it in on time and on or under cost. This edition contains ex

This text on control and estimation in distributed parameter systems relates frequency domain techniques to state-space or time domain approaches for infinite-dimensional systems, including design of

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing system

Illustrates the use of systems such as in-process control, quality auditing, and specifications, stressing a troubleshooting, cost-effective approach to product packaging for maximized early lead time

The collection consists of four parts: Part I presents three non-technical essays on economic development and economic systems. Four out of five essays in Part II deal with the theory and measurement of the so-called Index of Total Factor Productivity for several countries. The fifth essay is on the theory of index numbers. The first essay of Part III compares the American and Soviet patterns of economic development and finds that the path followed by each country might have been optimal for it at the time. The second essay develops a general theory of a producer cooperative. The third essay discusses a method for avoiding monopolistic exploitation, under either system, without price control. Part IV presents three applications of economic theory to historical problems - in particular, to serfdom and slavery. The first, on 'The Causes of Slavery or Serfdom', has become a classic. The second challenges the widely accepted view that Russian serfdom had become unprofitable for the serf-ow

This unique book provides a bridge between digital control theory and vehicle guidance and control practice. It presents practical techniques of digital redesign and direct discrete-time design suitab

Offering an introduction to the theory of impulse control in nonlinear systems, this book is useful as a text for a senior or graduate course. Chapters cover discrete-continuous systems with impulse c

The first motivation of Synthesis and Control of Discrete Event Systems is to inform the reader of recent developments and current trends in system synthesis. This is a field of active research aiming

Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on

If you want top grades and thorough understanding of feedback and control systems--both analog and digital--in less study time, this powerful study tool is the best tutor you can have It takes you ste

This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control syste