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Optimal Control Of A Discrete Time Stochastic System Linear In The State
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Book Synopsis Optimal Control of a Discrete Time Stochastic System Linear in the State by : Joseph L. Midler
Download or read book Optimal Control of a Discrete Time Stochastic System Linear in the State written by Joseph L. Midler and published by . This book was released on 1968 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered is a discrete-time stochastic control problem whose dynamic equations and loss function are linear in the state vector with random coefficients, but which may vary in a nonlinear, random manner with the control variables. The controls are constrained to lie in a given set. For this system it is shown that the optimal control or policy is independent of the value of the state. The result follows from a simple dynamic programming argument. Under suitable restrictions on the functions, the dynamic programming approach leads to efficient computational methods for obtaining the controls via a sequence of mathematical programming problems in fewer variables than the number of controls in the entire process. The result provides another instance of certainty equivalence for a sequential stochastic decision problem. The expectations of the random variables play the role of certainty equivalents in the sense that the optimal control can be found by solving a deterministic problem in which expectations replace the random quantities.
Author :Torsten Söderström Publisher :Springer Science & Business Media ISBN 13 :9781852336493 Total Pages :410 pages Book Rating :4.3/5 (364 download)
Book Synopsis Discrete-time Stochastic Systems by : Torsten Söderström
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.
Book Synopsis Optimal Control Methods for Linear Discrete-Time Economic Systems by : Y. Murata
Download or read book Optimal Control Methods for Linear Discrete-Time Economic Systems written by Y. Murata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: As our title reveals, we focus on optimal control methods and applications relevant to linear dynamic economic systems in discrete-time variables. We deal only with discrete cases simply because economic data are available in discrete forms, hence realistic economic policies should be established in discrete-time structures. Though many books have been written on optimal control in engineering, we see few on discrete-type optimal control. More over, since economic models take slightly different forms than do engineer ing ones, we need a comprehensive, self-contained treatment of linear optimal control applicable to discrete-time economic systems. The present work is intended to fill this need from the standpoint of contemporary macroeconomic stabilization. The work is organized as follows. In Chapter 1 we demonstrate instru ment instability in an economic stabilization problem and thereby establish the motivation for our departure into the optimal control world. Chapter 2 provides fundamental concepts and propositions for controlling linear deterministic discrete-time systems, together with some economic applica tions and numerical methods. Our optimal control rules are in the form of feedback from known state variables of the preceding period. When state variables are not observable or are accessible only with observation errors, we must obtain appropriate proxies for these variables, which are called "observers" in deterministic cases or "filters" in stochastic circumstances. In Chapters 3 and 4, respectively, Luenberger observers and Kalman filters are discussed, developed, and applied in various directions. Noticing that a separation principle lies between observer (or filter) and controller (cf.
Book Synopsis Linear Stochastic Control Systems by : Goong Chen
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.
Book Synopsis Stochastic Optimal Control by : Dimitri P. Bertsekas
Download or read book Stochastic Optimal Control written by Dimitri P. Bertsekas and published by . This book was released on 1961 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete-time Stochastic Systems by : Torsten Söderström
Download or read book Discrete-time Stochastic Systems written by Torsten Söderström and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 387 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.
Book Synopsis Optimal Control of Discrete Time Stochastic Systems by : C. Striebel
Download or read book Optimal Control of Discrete Time Stochastic Systems written by C. Striebel and published by Springer. This book was released on 2013-12-21 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Optimal Control by : Robert F. Stengel
Download or read book Stochastic Optimal Control written by Robert F. Stengel and published by Wiley-Interscience. This book was released on 1986-09-08 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents techniques for optimizing problems in dynamic systems with terminal and path constraints. Includes optimal feedback control, feedback control for linear systems, and regulator synthesis. Offers iterative methods for solving nonlinear control problems. Demonstrates how to apply optimal control in a practical fashion. Serves as a text for graduate controls courses as offered in aerospace, mechanical and chemical engineering departments.
Book Synopsis Optimal Control and Estimation by : Robert F. Stengel
Download or read book Optimal Control and Estimation written by Robert F. Stengel and published by Courier Corporation. This book was released on 1994-09-20 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An excellent introduction to optimal control and estimation theory and its relationship with LQG design. . . . invaluable as a reference for those already familiar with the subject." — Automatica. This highly regarded graduate-level text provides a comprehensive introduction to optimal control theory for stochastic systems, emphasizing application of its basic concepts to real problems. The first two chapters introduce optimal control and review the mathematics of control and estimation. Chapter 3 addresses optimal control of systems that may be nonlinear and time-varying, but whose inputs and parameters are known without error. Chapter 4 of the book presents methods for estimating the dynamic states of a system that is driven by uncertain forces and is observed with random measurement error. Chapter 5 discusses the general problem of stochastic optimal control, and the concluding chapter covers linear time-invariant systems. Robert F. Stengel is Professor of Mechanical and Aerospace Engineering at Princeton University, where he directs the Topical Program on Robotics and Intelligent Systems and the Laboratory for Control and Automation. He was a principal designer of the Project Apollo Lunar Module control system. "An excellent teaching book with many examples and worked problems which would be ideal for self-study or for use in the classroom. . . . The book also has a practical orientation and would be of considerable use to people applying these techniques in practice." — Short Book Reviews, Publication of the International Statistical Institute. "An excellent book which guides the reader through most of the important concepts and techniques. . . . A useful book for students (and their teachers) and for those practicing engineers who require a comprehensive reference to the subject." — Library Reviews, The Royal Aeronautical Society.
Book Synopsis Introduction to Stochastic Control Theory by : Karl J. Åström
Download or read book Introduction to Stochastic Control Theory written by Karl J. Åström and published by Courier Corporation. This book was released on 2012-05-11 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria, it covers discrete time as well as continuous time systems. The first three chapters provide motivation and background material on stochastic processes, followed by an analysis of dynamical systems with inputs of stochastic processes. A simple version of the problem of optimal control of stochastic systems is discussed, along with an example of an industrial application of this theory. Subsequent discussions cover filtering and prediction theory as well as the general stochastic control problem for linear systems with quadratic criteria. Each chapter begins with the discrete time version of a problem and progresses to a more challenging continuous time version of the same problem. Prerequisites include courses in analysis and probability theory in addition to a course in dynamical systems that covers frequency response and the state-space approach for continuous time and discrete time systems.
Book Synopsis Optimal Control of a Disrete Time Stochastic System Linear in the State by : Joseph L. Midler
Download or read book Optimal Control of a Disrete Time Stochastic System Linear in the State written by Joseph L. Midler and published by . This book was released on 1968 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimization of Stochastic Systems by : Masanao Aoki
Download or read book Optimization of Stochastic Systems written by Masanao Aoki and published by Elsevier. This book was released on 2016-06-03 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization of Stochastic Systems
Book Synopsis Control and System Theory of Discrete-Time Stochastic Systems by : Jan H. van Schuppen
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.
Book Synopsis Stochastic Optimal Control by : Dimitri P. Bertsekas
Download or read book Stochastic Optimal Control written by Dimitri P. Bertsekas and published by . This book was released on 1961 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sub-optimal Control of Linear Discrete-time Stochastic Systems Using Memory Elements by : James Richard Huddle
Download or read book Sub-optimal Control of Linear Discrete-time Stochastic Systems Using Memory Elements written by James Richard Huddle and published by . This book was released on 1966 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems by : Vasile Dragan
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.
Book Synopsis Optimization of Stochastic Discrete Systems and Control on Complex Networks by : Dmitrii Lozovanu
Download or read book Optimization of Stochastic Discrete Systems and Control on Complex Networks written by Dmitrii Lozovanu and published by Springer. This book was released on 2014-11-27 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book’s final chapter is devoted to finite horizon stochastic control problems and Markov decision processes. The algorithms developed represent a valuable contribution to the important field of computational network theory.
