Introduction to Mathematical Systems Theory

Linear Systems, Identification and Control

Author: Christiaan Heij,André C.M. Ran,F. van Schagen

Publisher: Springer Science & Business Media

ISBN: 3764375493

Category: Science

Page: 166

View: 1301

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.

Identification of Dynamic Systems

An Introduction with Applications

Author: Rolf Isermann,Marco Münchhof

Publisher: Springer Science & Business Media

ISBN: 9783540788799

Category: Technology & Engineering

Page: 705

View: 4109

Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.

Introduction to Mathematical Systems Theory

A Behavioral Approach

Author: J.C. Willems,J.W. Polderman

Publisher: Springer Science & Business Media

ISBN: 1475729537

Category: Mathematics

Page: 424

View: 8243

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.

System Identification

An Introduction

Author: Karel J. Keesman

Publisher: Springer Science & Business Media

ISBN: 9780857295224

Category: Technology & Engineering

Page: 323

View: 6080

System Identification shows the student reader how to approach the system identification problem in a systematic fashion. The process is divided into three basic steps: experimental design and data collection; model structure selection and parameter estimation; and model validation, each of which is the subject of one or more parts of the text. Following an introduction on system theory, particularly in relation to model representation and model properties, the book contains four parts covering: • data-based identification – non-parametric methods for use when prior system knowledge is very limited; • time-invariant identification for systems with constant parameters; • time-varying systems identification, primarily with recursive estimation techniques; and • model validation methods. A fifth part, composed of appendices, covers the various aspects of the underlying mathematics needed to begin using the text. The book uses essentially semi-physical or gray-box modeling methods although data-based, transfer-function system descriptions are also introduced. The approach is problem-based rather than rigorously mathematical. The use of finite input–output data is demonstrated for frequency- and time-domain identification in static, dynamic, linear, nonlinear, time-invariant and time-varying systems. Simple examples are used to show readers how to perform and emulate the identification steps involved in various control design methods with more complex illustrations derived from real physical, chemical and biological applications being used to demonstrate the practical applicability of the methods described. End-of-chapter exercises (for which a downloadable instructors’ Solutions Manual is available from fill in URL here) will both help students to assimilate what they have learned and make the book suitable for self-tuition by practitioners looking to brush up on modern techniques. Graduate and final-year undergraduate students will find this text to be a practical and realistic course in system identification that can be used for assessing the processes of a variety of engineering disciplines. System Identification will help academic instructors teaching control-related to give their students a good understanding of identification methods that can be used in the real world without the encumbrance of undue mathematical detail.

Linear Operators and Linear Systems

An Analytical Approach to Control Theory

Author: Jonathan R. Partington,C. M. Series

Publisher: Cambridge University Press

ISBN: 9780521546195

Category: Mathematics

Page: 166

View: 7661

"Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering."--Jacket.

An Introduction to Infinite-Dimensional Linear Systems Theory

Author: Ruth F. Curtain,Hans Zwart

Publisher: Springer Science & Business Media

ISBN: 146124224X

Category: Mathematics

Page: 698

View: 6739

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

Mathematical Control Theory

An Introduction

Author: Jerzy Zabczyk

Publisher: Springer Science & Business Media

ISBN: 9780817647339

Category: Science

Page: 260

View: 8751

Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. "Covers a remarkable number of topics....The book presents a large amount of material very well, and its use is highly recommended." --Bulletin of the AMS

Introduction to Dynamic Systems

Theory, Models, and Applications

Author: David G. Luenberger

Publisher: Wiley

ISBN: N.A

Category: Science

Page: 464

View: 6248

Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems.

Functional Analysis and Control Theory

Linear Systems

Author: Stefan Rolewicz

Publisher: Springer Science & Business Media

ISBN: 9789027721860

Category: Mathematics

Page: 524

View: 3348

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Mathematical Systems Theory I

Modelling, State Space Analysis, Stability and Robustness

Author: Diederich Hinrichsen,Anthony J. Pritchard

Publisher: Springer Science & Business Media

ISBN: 3540441255

Category: Mathematics

Page: 804

View: 9153

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.

A Mathematical Introduction to Control Theory

Second Edition

Author: Shlomo Engelberg

Publisher: World Scientific Publishing Company

ISBN: 178326781X

Category: Technology & Engineering

Page: 456

View: 5996

Striking a nice balance between mathematical rigor and engineering-oriented applications, this second edition covers the bedrock parts of classical control theory — the Routh-Hurwitz theorem and applications, Nyquist diagrams, Bode plots, root locus plots, and the design of controllers (phase-lag, phase-lead, lag-lead, and PID). It also covers three more advanced topics — non-linear control, modern control, and discrete-time control. This invaluable book makes effective use of MATLAB® as a tool in design and analysis. Containing 75 solved problems and 200 figures, this edition will be useful for junior and senior level university students in engineering who have a good knowledge of complex variables and linear algebra.

Discrete-Time Linear Systems

Theory and Design with Applications

Author: Guoxiang Gu

Publisher: Springer Science & Business Media

ISBN: 1461422817

Category: Technology & Engineering

Page: 452

View: 4981

Discrete-Time Linear Systems: Theory and Design with Applications combines system theory and design in order to show the importance of system theory and its role in system design. The book focuses on system theory (including optimal state feedback and optimal state estimation) and system design (with applications to feedback control systems and wireless transceivers, plus system identification and channel estimation).

Linear Control Systems

With solved problems and MATLAB examples

Author: Branislav Kisačanin,Gyan C. Agarwal

Publisher: Springer Science & Business Media

ISBN: 9780306467431

Category: Technology & Engineering

Page: 381

View: 6756

Anyone seeking a gentle introduction to the methods of modern control theory and engineering, written at the level of a first-year graduate course, should consider this book seriously. It contains: A generous historical overview of automatic control, from Ancient Greece to the 1970s, when this discipline matured into an essential field for electrical, mechanical, aerospace, chemical, and biomedical engineers, as well as mathematicians, and more recently, computer scientists; A balanced presentation of the relevant theory: the main state-space methods for description, analysis, and design of linear control systems are derived, without overwhelming theoretical arguments; Over 250 solved and exercise problems for both continuous- and discrete-time systems, often including MATLAB simulations; and Appendixes on MATLAB, advanced matrix theory, and the history of mathematical tools such as differential calculus, transform methods, and linear algebra. Another noteworthy feature is the frequent use of an inverted pendulum on a cart to illustrate the most important concepts of automatic control, such as: Linearization and discretization; Stability, controllability, and observability; State feedback, controller design, and optimal control; and Observer design, reduced order observers, and Kalman filtering. Most of the problems are given with solutions or MATLAB simulations. Whether the book is used as a textbook or as a self-study guide, the knowledge gained from it will be an excellent platform for students and practising engineers to explore further the recent developments and applications of control theory.

Linear Control Theory

The State Space Approach

Author: Frederick Walker Fairman

Publisher: John Wiley & Sons

ISBN: 9780471974895

Category: Mathematics

Page: 315

View: 9114

"Incorporating recent developments in control and systems research, Linear Control Theory provides the fundamental theoretical background needed to fully exploit control system design software ... Features include: The use of an easy to understand matrix variational technique to develop the time-invariant quadratic and LQG controllers, A step-by-step introduction to essential mathematical ideas as they are needed, motivating the reader to venture beyond basic concepts. The examination of linear system theory as it relates to control theory."--pub. desc.

Linear Systems Control

Deterministic and Stochastic Methods

Author: Elbert Hendricks,Ole Jannerup,Paul Haase Sørensen

Publisher: Springer Science & Business Media

ISBN: 3540784861

Category: Technology & Engineering

Page: 555

View: 4228

Linear Systems Control provides a very readable graduate text giving a good foundation for reading more rigorous texts. There are multiple examples, problems and solutions. This unique book successfully combines stochastic and deterministic methods.

Mathematical Control Theory

Deterministic Finite Dimensional Systems

Author: Eduardo D. Sontag

Publisher: Springer Science & Business Media

ISBN: 1461205778

Category: Mathematics

Page: 532

View: 2324

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Intelligent Control Systems Using Computational Intelligence Techniques

Author: A.E. Ruano

Publisher: IET

ISBN: 9780863414893

Category: Computers

Page: 454

View: 5209

Intelligent Control techniques are becoming important tools in both academia and industry. Methodologies developed in the field of soft-computing, such as neural networks, fuzzy systems and evolutionary computation, can lead to accommodation of more complex processes, improved performance and considerable time savings and cost reductions. Intelligent Control Systems using Computational Intellingence Techniques details the application of these tools to the field of control systems. Each chapter gives and overview of current approaches in the topic covered, with a set of the most important references in the field, and then details the author's approach, examining both the theory and practical applications.

Analysis and Design of Descriptor Linear Systems

Author: Guang-Ren Duan

Publisher: Springer Science & Business Media

ISBN: 9781441963970

Category: Mathematics

Page: 496

View: 9879

Descriptor linear systems theory is an important part in the general field of control systems theory, and has attracted much attention in the last two decades. In spite of the fact that descriptor linear systems theory has been a topic very rich in content, there have been only a few books on this topic. This book provides a systematic introduction to the theory of continuous-time descriptor linear systems and aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory. The clear representation of materials and a large number of examples make this book easy to understand by a large audience. General readers will find in this book a comprehensive introduction to the theory of descriptive linear systems. Researchers will find a comprehensive description of the most recent results in this theory and students will find a good introduction to some important problems in linear systems theory.