Deterministic Optimal Control
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Deterministic And Stochastic Optimal Control
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Author : Wendell H. Fleming
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Deterministic And Stochastic Optimal Control written by Wendell H. Fleming and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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 Optimal Control
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Author : H. Gardner Moyer
language : en
Publisher: Trafford Publishing
Release Date : 2003-03
Deterministic Optimal Control written by H. Gardner Moyer and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03 with Science categories.
This textbook is intended for physics students at the senior and graduate level. The first chapter employs Huygens' theory of wavefronts and wavelets to derive Hamilton's equations and the Hamilton-Jacobi equation. The final section presents a step-by-step precedure for the quanitzation of a Hamiltonian system. The remarkable congruence between particle dynaics and wave packets is shown. The second chapter presents sufficiency conditions for the standard case, broken, and singular extremals. Chapter III presents four schemes that can yield formal integrals of of Hamilton's equations- Killing's, Noether's, Poisson's, and Jacobi's. Chapter IV discusses iterative, numerical algorithms that converge to extremals. Three discontinuous problems are solved in Chapter V - refraction, jump discontinuities specified for state variables, and inequality contrainsts on state variables. The book contains many exercises and examples, in particular the geodesics of a Riemannian manifold.
Deterministic And Stochastic Optimal Control And Inverse Problems
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Author : Baasansuren Jadamba
language : en
Publisher: CRC Press
Release Date : 2021-12-15
Deterministic And Stochastic Optimal Control And Inverse Problems written by Baasansuren Jadamba and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-15 with Computers categories.
Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.
Optimal Design Of Control Systems
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Author : Gennadii E. Kolosov
language : en
Publisher: CRC Press
Release Date : 2020-08-27
Optimal Design Of Control Systems written by Gennadii E. Kolosov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Mathematics categories.
"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."
Infinite Horizon Optimal Control
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Author : Dean A. Carlson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Infinite Horizon Optimal Control written by Dean A. Carlson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals. For these problems the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts, referred to here as overtaking optimality, weakly overtaking optimality, agreeable plans, etc. , have been proposed. The motivation for studying these problems arises primarily from the economic and biological sciences where models of this type arise naturally. Indeed, any bound placed on the time hori zon is artificial when one considers the evolution of the state of an economy or species. The responsibility for the introduction of this interesting class of problems rests with the economists who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey [152] who, in his seminal work on the theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a Lagrange problem with unbounded time interval. The advent of modern control theory, particularly the formulation of the famous Maximum Principle of Pontryagin, has had a considerable impact on the treat ment of these models as well as optimization theory in general.
Stochastic Controls
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Author : Jiongmin Yong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Controls written by Jiongmin Yong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Stochastic Models Estimation And Control
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Author : Peter S. Maybeck
language : en
Publisher: Academic Press
Release Date : 1982-08-25
Stochastic Models Estimation And Control written by Peter S. Maybeck and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-08-25 with Mathematics categories.
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Deterministic Optimal Control Given Only A Partial Observation Of The Initial State
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Author : J. C. Allwright
language : en
Publisher:
Release Date : 1980
Deterministic Optimal Control Given Only A Partial Observation Of The Initial State written by J. C. Allwright and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Dynamic Programming And Stochastic Control
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Author : Bertsekas
language : en
Publisher: Academic Press
Release Date : 1976-11-26
Dynamic Programming And Stochastic Control written by Bertsekas and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-11-26 with Computers categories.
Dynamic Programming and Stochastic Control
Applied Optimal Control
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Author : A. E. Bryson
language : en
Publisher: Routledge
Release Date : 2018-05-04
Applied Optimal Control written by A. E. Bryson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Technology & Engineering categories.
This best-selling text focuses on the analysis and design of complicated dynamics systems. CHOICE called it ""a high-level, concise book that could well be used as a reference by engineers, applied mathematicians, and undergraduates. The format is good, the presentation clear, the diagrams instructive, the examples and problems helpful...References and a multiple-choice examination are included.