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: 6351

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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.

Foundations of Deterministic and Stochastic Control

Author: Jon H. Davis

Publisher: Springer Science & Business Media

ISBN: 1461200717

Category: Mathematics

Page: 426

View: 7196

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"This volume is a textbook on linear control systems with an emphasis on stochastic optimal control with solution methods using spectral factorization in line with the original approach of N. Wiener. Continuous-time and discrete-time versions are presented in parallel.... Two appendices introduce functional analytic concepts and probability theory, and there are 77 references and an index. The chapters (except for the last two) end with problems.... [T]he book presents in a clear way important concepts of control theory and can be used for teaching." —Zentralblatt Math "This is a textbook intended for use in courses on linear control and filtering and estimation on (advanced) levels. Its major purpose is an introduction to both deterministic and stochastic control and estimation. Topics are treated in both continuous time and discrete time versions.... Each chapter involves problems and exercises, and the book is supplemented by appendices, where fundamentals on Hilbert and Banach spaces, operator theory, and measure theoretic probability may be found. The book will be very useful for students, but also for a variety of specialists interested in deterministic and stochastic control and filtering." —Applications of Mathematics "The strength of the book under review lies in the choice of specialized topics it contains, which may not be found in this form elsewhere. Also, the first half would make a good standard course in linear control." —Journal of the Indian Institute of Science

Deterministic and Stochastic Optimal Control

Author: Wendell H. Fleming,Raymond W. Rishel

Publisher: Springer Science & Business Media

ISBN: 1461263808

Category: Mathematics

Page: 222

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This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.

Deterministic and Stochastic Time-Delay Systems

Author: El-Kebir Boukas,Zi-Kuan Liu

Publisher: Springer Science & Business Media

ISBN: 1461200776

Category: Mathematics

Page: 423

View: 366

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Most practical processes such as chemical reactor, industrial furnace, heat exchanger, etc., are nonlinear stochastic systems, which makes their con trol in general a hard problem. Currently, there is no successful design method for this class of systems in the literature. One common alterna tive consists of linearizing the nonlinear dynamical stochastic system in the neighborhood of an operating point and then using the techniques for linear systems to design the controller. The resulting model is in general an approximation of the real behavior of a dynamical system. The inclusion of the uncertainties in the model is therefore necessary and will certainly improve the performance of the dynamical system we want to control. The control of uncertain systems has attracted a lot of researchers from the control community. This topic has in fact dominated the research effort of the control community during the last two decades, and many contributions have been reported in the literature. Some practical dynamical systems have time delay in their dynamics, which makes their control a complicated task even in the deterministic case. Recently, the class ofuncertain dynamical deterministic systems with time delay has attracted some researchers, and some interesting results have been reported in both deterministic and stochastic cases. But wecan't claim that the control problem ofthis class ofsystems is completely solved; more work must be done for this class of systems.

Informatics in Control Automation and Robotics

Revised and Selected Papers from the International Conference on Informatics in Control Automation and Robotics 2009

Author: Juan Andrade Cetto,Joaquim Filipe,Jean-Louis Ferrier

Publisher: Springer Science & Business Media

ISBN: 9783642197307

Category: Technology & Engineering

Page: 354

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The present book includes a set of selected papers from the fourth “International Conference on Informatics in Control Automation and Robotics” (ICINCO 2009), held in Milan, Italy, from 2 to 5 July 2009. The conference was organized in three simultaneous tracks: “Intelligent Control Systems and Optimization”, “Robotics and Automation” and “Systems Modeling, Signal Processing and Control”. The book is based on the same structure. ICINCO received 365 paper submissions, not including those of workshops, from 55 countries, in all continents. After a double blind paper review performed by the Program Committee only 34 submissions were accepted as full papers and thus selected for oral presentation, leading to a full paper acceptance ratio of 9%. Additional papers were accepted as short papers and posters. A further refinement was made after the conference, based also on the assessment of presentation quality, so that this book includes the extended and revised versions of the very best papers of ICINCO 2009. Commitment to high quality standards is a major concern of ICINCO that will be maintained in the next editions of this conference, including not only the stringent paper acceptance ratios but also the quality of the program committee, keynote lectures, workshops and logistics.

Jump Linear Systems in Automatic Control

Author: M. Mariton

Publisher: Courier Corporation

ISBN: 9780824782009

Category: Technology & Engineering

Page: 299

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Jump linear systems in automatic control examine the mathematical framework of hybrid stochastic systems to solve practical problems. This timely resource bring together widely scattered information in two appendices that cover the principles of deterministic systems theory and stochastic processes and control-offering a convenient source of foundational information!

Linear Stochastic Control Systems

Author: Goong Chen,Guanrong Chen,Shih-Hsun Hsu

Publisher: CRC Press

ISBN: 9780849380754

Category: Business & Economics

Page: 400

View: 3709

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Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.

Theory of Hybrid Systems: Deterministic and Stochastic

Author: Mohamad S. Alwan,Xinzhi Liu

Publisher: Springer

ISBN: 9789811080456

Category: Technology & Engineering

Page: 241

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This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin–Lyapunov methods to investigate the systems’ properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.

Subspace Identification for Linear Systems

Theory — Implementation — Applications

Author: Peter van Overschee,B.L. de Moor

Publisher: Springer Science & Business Media

ISBN: 1461304652

Category: Technology & Engineering

Page: 272

View: 377

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Subspace Identification for Linear Systems focuses on the theory, implementation and applications of subspace identification algorithms for linear time-invariant finite- dimensional dynamical systems. These algorithms allow for a fast, straightforward and accurate determination of linear multivariable models from measured input-output data. The theory of subspace identification algorithms is presented in detail. Several chapters are devoted to deterministic, stochastic and combined deterministic-stochastic subspace identification algorithms. For each case, the geometric properties are stated in a main 'subspace' Theorem. Relations to existing algorithms and literature are explored, as are the interconnections between different subspace algorithms. The subspace identification theory is linked to the theory of frequency weighted model reduction, which leads to new interpretations and insights. The implementation of subspace identification algorithms is discussed in terms of the robust and computationally efficient RQ and singular value decompositions, which are well-established algorithms from numerical linear algebra. The algorithms are implemented in combination with a whole set of classical identification algorithms, processing and validation tools in Xmath's ISID, a commercially available graphical user interface toolbox. The basic subspace algorithms in the book are also implemented in a set of Matlab files accompanying the book. An application of ISID to an industrial glass tube manufacturing process is presented in detail, illustrating the power and user-friendliness of the subspace identification algorithms and of their implementation in ISID. The identified model allows for an optimal control of the process, leading to a significant enhancement of the production quality. The applicability of subspace identification algorithms in industry is further illustrated with the application of the Matlab files to ten practical problems. Since all necessary data and Matlab files are included, the reader can easily step through these applications, and thus get more insight in the algorithms. Subspace Identification for Linear Systems is an important reference for all researchers in system theory, control theory, signal processing, automization, mechatronics, chemical, electrical, mechanical and aeronautical engineering.

Optimal Design of Control Systems

Stochastic and Deterministic Problems (Pure and Applied Mathematics: A Series of Monographs and Textbooks/221)

Author: Gennadii E. Kolosov

Publisher: CRC Press

ISBN: 9780824775377

Category: Technology & Engineering

Page: 424

View: 6262

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"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."

Optimal Control and Estimation

Author: Robert F. Stengel

Publisher: Courier Corporation

ISBN: 0486134814

Category: Mathematics

Page: 672

View: 7871

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Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

Controlled Stochastic Processes

Author: I. I. Gihman,A. V. Skorohod

Publisher: Springer Science & Business Media

ISBN: 146126202X

Category: Mathematics

Page: 237

View: 9579

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The theory of controlled processes is one of the most recent mathematical theories to show very important applications in modern engineering, parti cularly for constructing automatic control systems, as well as for problems of economic control. However, actual systems subject to control do not admit a strictly deterministic analysis in view of random factors of various kinds which influence their behavior. Such factors include, for example, random noise occurring in the electrical system, variations in the supply and demand of commodities, fluctuations in the labor force in economics, and random failures of components on an automated line. The theory of con trolled processes takes the random nature of the behavior of a system into account. In such cases it is natural, when choosing a control strategy, to proceed from the average expected result, taking note of all the possible variants of the behavior of a controlled system. An extensive literature is devoted to various economic and engineering systems of control (some of these works are listed in the Bibliography). is no text which adequately covers the general However, as of now there mathematical theory of controlled processes. The authors ofthis monograph have attempted to fill this gap. In this volume the general theory of discrete-parameter (time) controlled processes (Chapter 1) and those with continuous-time (Chapter 2), as well as the theory of controlled stochastic differential equations (Chapter 3), are presented.

Advances in Deterministic and Stochastic Analysis

Author: N. M. Chuong

Publisher: World Scientific

ISBN: 9812770496

Category: Deterministic chaos

Page: 372

View: 1020

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This volume collects articles in pure and applied analysis, partial differential equations, geometric analysis and stochastic and infinite-dimensional analysis. In particular, the contributors discuss integral and pseudo-differential operators, which play an important role in partial differential equations. Other methods of solving the partial differential equations are considered, such as the min-max approach to variational problems and boundary value problems. The foundations of quantum mechanics from the viewpoints of infinite-dimensional spaces and Bell''s inequality and contraction are also mentioned.

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: 2910

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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.

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Author: Leonid Shaikhet

Publisher: Springer Science & Business Media

ISBN: 3319001019

Category: Technology & Engineering

Page: 342

View: 4667

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Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.

Continuous-time Stochastic Control and Optimization with Financial Applications

Author: Huyên Pham

Publisher: Springer Science & Business Media

ISBN: 3540895000

Category: Mathematics

Page: 232

View: 433

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Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Dynamic Management Decision and Stochastic Control Processes

Author: Toshio Odanaka

Publisher: World Scientific

ISBN: 9789810200923

Category: Business & Economics

Page: 221

View: 1304

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This book treats stochastic control theory and its applications in management. The main numerical techniques necessary for such applications are presented. Several advanced topics leading to optimal processes are dismissed. The book also considers the theory of some stochastic control processes and several applications to illustrate the ideas.

Mono- and Multivariable Control and Estimation

Linear, Quadratic and LMI Methods

Author: Eric Ostertag

Publisher: Springer Science & Business Media

ISBN: 9783642137341

Category: Language Arts & Disciplines

Page: 360

View: 9135

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This book presents the various design methods of a state-feedback control law and of an observer. The considered systems are of continuous-time and of discrete-time nature, monovariable or multivariable, the last ones being of main consideration. Three different approaches are described: • Linear design methods, with an emphasis on decoupling strategies, and a general formula for multivariable controller or observer design; • Quadratic optimization methods: Linear Quadratic Control (LQC), optimal Kalman filtering, Linear Quadratic Gaussian (LQG) control; • Linear matrix inequalities (LMIs) to solve linear and quadratic problems. The duality between control and observation is taken to advantage and extended up to the mathematical domain. A large number of exercises, all given with their detailed solutions, mostly obtained with MATLAB, reinforce and exemplify the practical orientation of this book. The programs, created by the author for their solving, are available on the Internet sites of Springer and of MathWorks for downloading. This book is targeted at students of Engineering Schools or Universities, at the Master’s level, at engineers desiring to design and implement innovative control methods, and at researchers.

Optimal Control Of Singularly Perturbed Linear Systems And Applications

Author: Zoran Gajic

Publisher: CRC Press

ISBN: 0824744853

Category: Technology & Engineering

Page: 326

View: 9621

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Highlighing the Hamiltonian approach to singularly perturbed linear optimal control systems, this volume develops parallel algorithms in independent slow and fast time scales to solve various optimal linear control and filtering problems.