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Author: J.C. Willems Publisher: Springer Science & Business Media ISBN: 1475729537 Category : Mathematics Languages : en Pages : 446
Book Description
Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
Author: J.C. Willems Publisher: Springer Science & Business Media ISBN: 1475729537 Category : Mathematics Languages : en Pages : 446
Book Description
Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
Author: Christiaan Heij Publisher: Springer Nature ISBN: 3030596540 Category : Science Languages : en Pages : 195
Book Description
This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering. The focus is on discrete time systems, which are the most relevant in business applications, as opposed to continuous time systems, requiring less mathematical preliminaries. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation. This second edition has been updated and slightly expanded. In addition, supplementary material containing the exercises is now available on the Springer Link's book website.
Author: Christiaan Heij Publisher: Springer Science & Business Media ISBN: 3764375493 Category : Science Languages : en Pages : 169
Book Description
This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering; the focus is on discrete time systems. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation.
Author: Sifeng Liu Publisher: Springer Science & Business Media ISBN: 364216157X Category : Technology & Engineering Languages : en Pages : 391
Book Description
Due to inherent limitations in human sensing organs, most data collected for various purposes contain uncertainties. Even at the rare occasions when accurate data are available, the truthful predictions derived on the data tend to create chaotic consequences. So, to effectively process and make sense out of available data, we need methods to deal with uncertainty inherently existing inside the data. The intent of this monograph is to explore the fundamental theory, methods, and techniques of practical application of grey systems theory, initiated by Professor Deng Julong in 1982. This volume presents most of the recent advances of the theory accomplished by scholars from around the world. From studying this book, the reader will not only acquire an overall knowledge of this new theory but also be able to follow the most current research activities. All examples presented are based on practical applications of the theory when urgent real-life problems had to be addressed. Last but not the least, this book concludes with three appendices. The first one compares grey systems theory and interval analysis while revealing the fact that interval analysis is a part of grey mathematics. The second appendix presents an array of different approaches of studying uncertainties. And, the last appendix shows how uncertainties appear using general systems approach.
Author: Diederich Hinrichsen Publisher: Springer Science & Business Media ISBN: 3540441255 Category : Mathematics Languages : en Pages : 818
Book Description
This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions.
Author: Yi Lin Publisher: Springer Science & Business Media ISBN: 0306469626 Category : Science Languages : en Pages : 386
Book Description
As suggested by the title of this book, I will present a collection of coherently related applications and a theoretical development of a general systems theory. Hopefully, this book will invite all readers to sample an exciting and challenging (even fun!) piece of interdisciplinary research, that has characterized the scientific and technological achievements of the twentieth century. And, I hope that many of them will be motivated to do additional reading and to contribute to topics along the lines described in the following pages. Since the applications in this volume range through many scientific disciplines, from sociology to atomic physics, from Einstein’s relativity theory to Dirac’s quan tum mechanics, from optimization theory to unreasonable effectiveness of mathe matics to foundations of mathematical modeling, from general systems theory to Schwartz’s distributions, special care has been given to write each application in a language appropriate to that field. That is, mathematical symbols and abstractions are used at different levels so that readers in various fields will find it possible to read. Also, because of the wide range of applications, each chapter has been written so that, in general, there is no need to reference a different chapter in order to understand a specific application. At the same time, if a reader has the desire to go through the entire book without skipping any chapter, it is strongly suggested to refer back to Chapters 2 and 3 as often as possible.
Author: Bruno Carpentieri Publisher: BoD – Books on Demand ISBN: 1839691239 Category : Mathematics Languages : en Pages : 132
Book Description
The theory of modern dynamical systems dates back to 1890 with studies by Poincaré on celestial mechanics. The tradition was continued by Birkhoff in the United States with his pivotal work on periodic orbits, and by the Moscow School in Russia (Liapunov, Andronov, Pontryagin). In the 1960s the field was revived by the emergence of the theory of chaotic attractors, and in modern years by accurate computer simulations. This book provides an overview of recent developments in the theory of dynamical systems, presenting some significant advances in the definition of new models, computer algorithms, and applications. Researchers, engineers and graduate students in both pure and applied mathematics will benefit from the chapters collected in this volume.
Author: Joachim Rosenthal Publisher: Springer Science & Business Media ISBN: 0387216960 Category : Science Languages : en Pages : 508
Book Description
This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
Author: Preston C. Hammer Publisher: Penn State University Press ISBN: Category : Mathematics Languages : en Pages : 198
Book Description
The patterns that have emerged from recent attempts to use mathematics to discuss complex phenomena have led to the development of a new discipline--mathematical systems theory. This theory arises from models of the important interactions in real systems. Mathematicians, engineers, and technically-oriented administrators will find this new series-which describes in detail the latest views on real systems and the uses of formal systems-of great value. Four main areas are investigated in the first volume of the series: theory of finite automata in engineering systems; control systems; computer linguistics; and global principles concerning systems. Examples and applications are provided throughout this work. Contributors: Preston G. Hammer (Editor), Head, Computer Science Department, The Pennsylvania State University. Alan J. Perlis, Head, Computer Science Department, Case Institute of Technology, Former President, Association for Computing Machinery. M.D. Mesarovich, Director, Systems Research Institute, Case Institute of Technology, Editor, Journal of Mathematical Systems Theory. A.W. Wymore, Head, Systems Engineering Department, University of Arizona.
Author: C. Heij Publisher: Birkhäuser ISBN: Category : Computers Languages : en Pages : 182
Book Description
This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering. The focus is on discrete time systems, which are the most relevant in business applications, as opposed to continuous time systems, requiring less mathematical preliminaries. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation.
Author: J.C. Willems
Author: J.C. Willems
Author: Christiaan Heij
Author: Christiaan Heij
Author: Sifeng Liu
Author: Diederich Hinrichsen
Author: Yi Lin
Author: Bruno Carpentieri
Author: Joachim Rosenthal
Author: Preston C. Hammer
Author: C. Heij