Download or read book Linear Stochastic Control Systems written by Goong Chen and published by CRC Press. This book was released on 1995-07-12 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Systems written by P. R. Kumar and published by SIAM. This book was released on 2015-12-15 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its origins in the 1940s, the subject of decision making under uncertainty has grown into a diversified area with application in several branches of engineering and in those areas of the social sciences concerned with policy analysis and prescription. These approaches required a computing capacity too expensive for the time, until the ability to collect and process huge quantities of data engendered an explosion of work in the area. This book provides succinct and rigorous treatment of the foundations of stochastic control; a unified approach to filtering, estimation, prediction, and stochastic and adaptive control; and the conceptual framework necessary to understand current trends in stochastic control, data mining, machine learning, and robotics.

Download or read book Linear Stochastic Systems written by Peter E. Caines and published by SIAM. This book was released on 2018-06-12 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships. The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including the fundamentals of stochastic processes and the construction of stochastic systems; an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and a presentation of stochastic adaptive control theory. Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.

Download or read book Linear Stochastic Systems written by Anders Lindquist and published by Springer. This book was released on 2015-04-24 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.

Download or read book Linear Systems Control written by Elbert Hendricks and published by Springer Science & Business Media. This book was released on 2008-10-13 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar. In this way it is easy to immediately apply the theory to the understanding and control of ordinary systems. Application engineers, working in industry, will also find this book interesting and useful for this reason. In line with the approach set forth above, the book first deals with the modeling of systems in state space form. Both transfer function and differential equation modeling methods are treated with many examples. Linearization is treated and explained first for very simple nonlinear systems and then more complex systems. Because computer control is so fundamental to modern applications, discrete time modeling of systems as difference equations is introduced immediately after the more intuitive differential equation models. The conversion of differential equation models to difference equations is also discussed at length, including transfer function formulations. A vital problem in modern control is how to treat noise in control systems. Nevertheless this question is rarely treated in many control system textbooks because it is considered to be too mathematical and too difficult in a second course on controls. In this textbook a simple physical approach is made to the description of noise and stochastic disturbances which is easy to understand and apply to common systems. This requires only a few fundamental statistical concepts which are given in a simple introduction which lead naturally to the fundamental noise propagation equation for dynamic systems, the Lyapunov equation. This equation is given and exemplified both in its continuous and discrete time versions. With the Lyapunov equation available to describe state noise propagation, it is a very small step to add the effect of measurements and measurement noise. This gives immediately the Riccati equation for optimal state estimators or Kalman filters. These important observers are derived and illustrated using simulations in terms which make them easy to understand and easy to apply to real systems. The use of LQR regulators with Kalman filters give LQG (Linear Quadratic Gaussian) regulators which are introduced at the end of the book. Another important subject which is introduced is the use of Kalman filters as parameter estimations for unknown parameters. The textbook is divided into 7 chapters, 5 appendices, a table of contents, a table of examples, extensive index and extensive list of references. Each chapter is provided with a summary of the main points covered and a set of problems relevant to the material in that chapter. Moreover each of the more advanced chapters (3 - 7) are provided with notes describing the history of the mathematical and technical problems which lead to the control theory presented in that chapter. Continuous time methods are the main focus in the book because these provide the most direct connection to physics. This physical foundation allows a logical presentation and gives a good intuitive feel for control system construction. Nevertheless strong attention is also given to discrete time systems. Very few proofs are included in the book but most of the important results are derived. This method of presentation makes the text very readable and gives a good foundation for reading more rigorous texts. A complete set of solutions is available for all of the problems in the text. In addition a set of longer exercises is available for use as Matlab/Simulink ‘laboratory exercises’ in connection with lectures. There is material of this kind for 12 such exercises and each exercise requires about 3 hours for its solution. Full written solutions of all these exercises are available.

Download or read book Foundations of Deterministic and Stochastic Control written by Jon H. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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

Download or read book Mathematical Methods in Robust Control of Discrete Time Linear Stochastic Systems written by Vasile Dragan and published by Springer Science & Business Media. This book was released on 2009-11-10 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Control of Partially Observable Systems written by Alain Bensoussan and published by Cambridge University Press. This book was released on 2004-11-11 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of stochastic control of partially observable systems plays an important role in many applications. All real problems are in fact of this type, and deterministic control as well as stochastic control with full observation can only be approximations to the real world. This justifies the importance of having a theory as complete as possible, which can be used for numerical implementation. This book first presents those problems under the linear theory that may be dealt with algebraically. Later chapters discuss the nonlinear filtering theory, in which the statistics are infinite dimensional and thus, approximations and perturbation methods are developed.

Download or read book Stochastic Linear Quadratic Optimal Control Theory Open Loop and Closed Loop Solutions written by Jingrui Sun and published by Springer Nature. This book was released on 2020-06-29 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Download or read book Rational Matrix Equations in Stochastic Control written by Tobias Damm and published by Springer Science & Business Media. This book was released on 2004-01-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intended for researchers, graduate students and engineers in control theory and applied linear algebra.

Download or read book Discrete time Stochastic Systems written by Torsten Söderström and published by Springer Science & Business Media. This book was released on 2002-07-26 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Download or read book Stochastic Controls written by Jiongmin Yong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.

Download or read book Stochastic Distribution Control System Design written by Lei Guo and published by Springer. This book was released on 2012-07-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A recent development in SDC-related problems is the establishment of intelligent SDC models and the intensive use of LMI-based convex optimization methods. Within this theoretical framework, control parameter determination can be designed and stability and robustness of closed-loop systems can be analyzed. This book describes the new framework of SDC system design and provides a comprehensive description of the modelling of controller design tools and their real-time implementation. It starts with a review of current research on SDC and moves on to some basic techniques for modelling and controller design of SDC systems. This is followed by a description of controller design for fixed-control-structure SDC systems, PDF control for general input- and output-represented systems, filtering designs, and fault detection and diagnosis (FDD) for SDC systems. Many new LMI techniques being developed for SDC systems are shown to have independent theoretical significance for robust control and FDD problems.

Download or read book Optimal Control and Estimation written by Robert F. Stengel and published by Courier Corporation. This book was released on 2012-10-16 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems. "Invaluable as a reference for those already familiar with the subject." — Automatica.

Download or read book Control and System Theory of Discrete Time Stochastic Systems written by Jan H. van Schuppen and published by Springer Nature. This book was released on 2021-08-02 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.​

Download or read book Stochastic Evolution Systems written by Boris L. Rozovsky and published by Springer. This book was released on 2018-10-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

Download or read book Deterministic and Stochastic Optimal Control written by Wendell H. Fleming and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.