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: 1240

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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: 3255

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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

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

View: 938

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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.

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: 7074

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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.

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.

Regelung elektrischer Antriebe

Author: Werner Leonhard

Publisher: Springer-Verlag

ISBN: 3642573282

Category: Technology & Engineering

Page: 462

View: 7827

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Leistungselektronisch gespeiste und mikroelektronisch geregelte elektrische Antriebe sind dynamisch hochwertige und universell einsetzbare elektromechanische Energiewandler, die heute in vielfältigen Ausführungsformen in weiten Bereichen von Drehmoment, Drehzahl und Leistung zur Verfügung stehen. Von besonderer Bedeutung sind kommutatorlose Drehstrom-Regelantriebe, die erst mit vektoriellen Verfahren und einer digital verwirklichten Regelungstechnik möglich wurden. Das Buch enthält eine zusammenfassende theoretische Darstellung elektrischer Regelantriebe einschließlich der leistungselektronischen Umrichter, von klassischen Gleichstromantrieben bis zu digital geregelten Drehstromantrieben. Die beschriebenen Verfahren werden durch experimentelle Ergebnisse belegt; Anwendungen sind anhand von Beispielen diskutiert.

Theory of Hybrid Systems: Deterministic and Stochastic

Author: Mohamad S. Alwan,Xinzhi Liu

Publisher: Springer

ISBN: 9811080461

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.

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: 1845

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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."

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!

Introduction to Stochastic Control Theory

Author: Karl J. Åström

Publisher: Courier Corporation

ISBN: 0486138275

Category: Technology & Engineering

Page: 320

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Exploration of stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria; covers discrete time and continuous time systems. 1970 edition.

Optimal Control Of Singularly Perturbed Linear Systems And Applications

Author: Zoran Gajic

Publisher: CRC Press

ISBN: 0824744853

Category: Technology & Engineering

Page: 326

View: 5855

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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.

Computation in Constrained Stochastic Model Predictive Control of Linear Systems

Author: N.A

Publisher: Stanford University

ISBN: N.A

Category:

Page: N.A

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Despite its sub-optimality, Model Predictive Control (MPC) has received much attention over the recent decades due to its ability to handle constraints. In particular, stochastic MPC, which includes uncertainty in the system dynamics, is one of the most active recent research topics in MPC. In this dissertation, we focus on (1) increasing computation speed of constrained stochastic MPC of linear systems with additive noise and, (2) improving the accuracy of an approximate solution involving systems with additive and multiplicative noise. Constrained MPC for linear systems with additive noise has been successfully formulated as a semidefinite programming problem (SDP) using the Youla parameterization or innovation feedback and linear matrix inequalities. Unfortunately, this method can be prohibitively slow even for problems with moderate size state. Thus, in this thesis we develop an interior point algorithm which can more efficiently solve the problem. This algorithm converts the stochastic problem into a deterministic one using the mean and the covariance matrix as the system state and using affine feedback. A line search interior point method is then directly applied to the nonlinear deterministic optimization problem. In the process, we take advantage of a recursive structure that appears when a control problem is solved via the line search interior point method in order to decrease the algorithmic complexity of the solution. We compare the computation time and complexity of our algorithm against an SDP solver. The second part of the dissertation deals with systems with additive and multiplicative noise under probabilistic constraints. This class of systems differs from the additive noise case in that the probability distribution of a state is neither Gaussian nor known in closed form. This causes a problem when the probability constraints are dealt with. In previous studies, this problem has been tackled by approximating the state as a Gaussian random variable or by approximating the probability bound as an ellipsoid. In this dissertation, we use the Cornish-Fisher expansion to approximate the probability bounds of the constraints. Since the Cornish-Fisher expansion utilizes quantile values with the first several moments, the probabilistic constraints have the same form as those in the additive noise case when the constraints are converted to deterministic ones. This makes the procedure smooth when we apply the developed algorithm to a linear system with multiplicative noise. Moreover, we can easily extend the application of the algorithm to a linear system with additive plus multiplicative noise.

Mathematical Methods in Robust Control of Linear Stochastic Systems

Author: Vasile Dragan,Toader Morozan,Adrian-Mihail Stoica

Publisher: Springer Science & Business Media

ISBN: 0387359249

Category: Science

Page: 312

View: 7601

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The book covers the necessary pre-requisites from probability theory, stochastic processes, stochastic integrals and stochastic differential equations. It includes detailed treatment of the fundamental properties of stochastic systems subjected both to multiplicative white noise and to jump Markovian perturbations. Systematic presentation leads the reader in a natural way to the original results. New theoretical results accompanied by detailed numerical examples, and the book proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations.

Linear Stochastic Control Systems

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

Publisher: CRC Press

ISBN: 9780849380754

Category: Business & Economics

Page: 400

View: 9076

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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.

Stochastic Dynamics and Control

Author: Jian-Qiao Sun

Publisher: Elsevier

ISBN: 9780080463988

Category: Mathematics

Page: 426

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This book is a result of many years of author’s research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations. · Comprehensive review of probability theory, and stochastic processes · Random vibrations · Structural reliability and fatigue, Non-Gaussian fatigue · Monte Carlo methods · Stochastic calculus and engineering applications · Stochastic feedback controls and optimal controls · Stochastic sliding mode controls · Feedback control of stochastic time-delayed systems · Probability density tracking control

Complex Systems

Fractionality, Time-delay and Synchronization

Author: Albert C. J. Luo,Jian-Qiao Sun

Publisher: Springer Science & Business Media

ISBN: 3642175937

Category: Science

Page: 275

View: 8369

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"Complex Systems: Fractionality, Time-delay and Synchronization" covers the most recent developments and advances in the theory and application of complex systems in these areas. Each chapter was written by scientists highly active in the field of complex systems. The book discusses a new treatise on fractional dynamics and control, as well as the new methods for differential delay systems and control. Lastly, a theoretical framework for the complexity and synchronization of complex system is presented. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. It can also serve as a reference book for graduate students in physics, applied mathematics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Jian-Qiao Sun is a Professor at the University of California, Merced, USA.

Linear Systems

Optimal and Robust Control

Author: Alok Sinha

Publisher: CRC Press

ISBN: 1420008889

Category: Technology & Engineering

Page: 488

View: 4308

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Balancing rigorous theory with practical applications, Linear Systems: Optimal and Robust Control explains the concepts behind linear systems, optimal control, and robust control and illustrates these concepts with concrete examples and problems. Developed as a two-course book, this self-contained text first discusses linear systems, including controllability, observability, and matrix fraction description. Within this framework, the author develops the ideas of state feedback control and observers. He then examines optimal control, stochastic optimal control, and the lack of robustness of linear quadratic Gaussian (LQG) control. The book subsequently presents robust control techniques and derives H∞ control theory from the first principle, followed by a discussion of the sliding mode control of a linear system. In addition, it shows how a blend of sliding mode control and H∞ methods can enhance the robustness of a linear system. By learning the theories and algorithms as well as exploring the examples in Linear Systems: Optimal and Robust Control, students will be able to better understand and ultimately better manage engineering processes and systems.

Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems

Author: Vasile Dragan,Toader Morozan,Adrian-Mihail Stoica

Publisher: Springer Science & Business Media

ISBN: 1441906304

Category: Mathematics

Page: 346

View: 2223

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In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. The theory is a continuation of the authors’ work presented in their previous book entitled "Mathematical Methods in Robust Control of Linear Stochastic Systems" published by Springer in 2006. Key features: - Provides a common unifying framework for discrete-time stochastic systems corrupted with both independent random perturbations and with Markovian jumps which are usually treated separately in the control literature; - Covers preliminary material on probability theory, independent random variables, conditional expectation and Markov chains; - Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations; - Leads the reader in a natural way to the original results through a systematic presentation; - Presents new theoretical results with detailed numerical examples. The monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.