Deterministic and Stochastic Optimal Control

Deterministic and Stochastic Optimal Control

This book may be regarded as consisting of two parts.

Author: Wendell H. Fleming

Publisher: Springer Science & Business Media

ISBN: 9781461263807

Category: Mathematics

Page: 222

View: 107

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.
Categories: Mathematics

Deterministic and Stochastic Optimal Control

Deterministic and Stochastic Optimal Control

"The first part of this book presents the essential topics for an introduction to deterministic optimal control theory.

Author: Wendell Helms Fleming

Publisher:

ISBN: CORNELL:31924000472690

Category: Commande, Théorie de la

Page: 222

View: 137

"The first part of this book presents the essential topics for an introduction to deterministic optimal control theory. The second part introduces stochastic optimal control for Markov diffusion processes. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle"--Publisher description.
Categories: Commande, Théorie de la

Infinite Horizon Optimal Control

Infinite Horizon Optimal Control

This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals.

Author: Dean A. Carlson

Publisher: Springer Science & Business Media

ISBN: 9783642767555

Category: Business & Economics

Page: 332

View: 646

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.
Categories: Business & Economics

Deterministic and Stochastic Optimal Control and Inverse Problems

Deterministic and Stochastic Optimal Control and Inverse Problems

This edited volume comprises invited contributions from world-renowned researchers in the subject of stochastic control and inverse problems.

Author: Baasansuren Jadamba

Publisher: CRC Press

ISBN: 0367506300

Category: Inverse problems (Differential equations)

Page: 390

View: 470

This edited volume comprises invited contributions from world-renowned researchers in the subject of stochastic control and inverse problems. There are several contributions on stochastic optimal control and stochastic inverse problems covering different aspects of the theory, numerical methods, and applications.
Categories: Inverse problems (Differential equations)

Deterministic Methods in Stochastic Optimal Control

Deterministic Methods in Stochastic Optimal Control

In this paper a new approach to the control of systems represented by stochastic differential equations (SDEs) is developed in which stochastic control is viewed as deterministic control with a particular form of constraint structure.

Author: Mark H. A. Davis

Publisher:

ISBN: OCLC:59904414

Category: Mathematical statistics

Page:

View: 166

Categories: Mathematical statistics

Foundations of Deterministic and Stochastic Control

Foundations of Deterministic and Stochastic Control

"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.

Author: Jon H. Davis

Publisher: Springer Science & Business Media

ISBN: 9781461200710

Category: Mathematics

Page: 426

View: 397

"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
Categories: Mathematics

Stochastic Optimal Control The Discrete Time Case

Stochastic Optimal Control  The Discrete Time Case

Apart from anything else, the book serves as an excellent introduction to the arcane world of analytic sets and other lesser known byways of measure theory.

Author: Dimitri P. Bertsekas

Publisher: Athena Scientific

ISBN: 9781886529038

Category: Mathematics

Page: 330

View: 678

This research monograph, first published in 1978 by Academic Press, remains the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues. It is an excellent supplement to the first author's Dynamic Programming and Optimal Control (Athena Scientific, 2018). Review of the 1978 printing:"Bertsekas and Shreve have written a fine book. The exposition is extremely clear and a helpful introductory chapter provides orientation and a guide to the rather intimidating mass of literature on the subject. Apart from anything else, the book serves as an excellent introduction to the arcane world of analytic sets and other lesser known byways of measure theory." Mark H. A. Davis, Imperial College, in IEEE Trans. on Automatic Control Among its special features, the book: 1) Resolves definitively the mathematical issues of discrete-time stochastic optimal control problems, including Borel models, and semi-continuous models 2) Establishes the most general possible theory of finite and infinite horizon stochastic dynamic programming models, through the use of analytic sets and universally measurable policies 3) Develops general frameworks for dynamic programming based on abstract contraction and monotone mappings 4) Provides extensive background on analytic sets, Borel spaces and their probability measures 5) Contains much in depth research not found in any other textbook
Categories: Mathematics

Optimal Design of Control Systems

Optimal Design of Control Systems

"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.

Author: Gennadii E. Kolosov

Publisher: CRC Press

ISBN: 9781000146752

Category: Mathematics

Page: 424

View: 224

"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."
Categories: Mathematics

Perturbation Methods in Optimal Control

Perturbation Methods in Optimal Control

The purpose of this book is to describe, analyse and to some extent generalise the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations.

Author: Alain Bensoussan

Publisher:

ISBN: 2040164693

Category: Control theory

Page: 573

View: 471

Perturbation methods provide a powerful technique for treating many problems of applied mathematics. These problems occur very frequently in solid and fluid mechanics, in physics, in engineering and also in economics. The purpose of this book is to describe, analyse and to some extent generalise the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations. The author aims to present a unified account of the available results. The first two chapters cover the main results in deterministic and stochastic optimal control theory, and in ergodic control theory. The remaining chapters deal with the applications of perturbation methods in deterministic and stochastic optimal control. Regular and singular perturbations are treated separately. Two broad categories of methods are used: the theory of necessary conditions, leading to Pontryagin's maximum principle, and the theory of sufficient conditions, leading to dynamic programming. The book will be of great interest to researchers and practitioners working in applied mathematics, solid and fluid mechanics, engineering, physics and economics.
Categories: Control theory

Stochastic Controls

Stochastic Controls

This is known as a Hamilton-Jacobi-Bellman (HJB) equation.

Author: Jiongmin Yong

Publisher: Springer Science & Business Media

ISBN: 9781461214663

Category: Mathematics

Page: 439

View: 988

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.
Categories: Mathematics

Infinite Horizon Optimal Control

Infinite Horizon Optimal Control

This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals.

Author: Dean A Carlson

Publisher:

ISBN: 3642767567

Category:

Page: 352

View: 956

Categories:

Trends in Control Theory and Partial Differential Equations

Trends in Control Theory and Partial Differential Equations

The book will be of interest for both researchers and graduate students working in these areas. This book presents cutting-edge contributions in the areas of control theory and partial differential equations.

Author: Fatiha Alabau-Boussouira

Publisher: Springer

ISBN: 9783030179496

Category: Mathematics

Page: 276

View: 615

This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
Categories: Mathematics

Stochastic Optimal Control of Structures

Stochastic Optimal Control of Structures

This book proposes, for the first time, a basic formulation for structural control that takes into account the stochastic dynamics induced by engineering excitations in the nature of non-stationary and non-Gaussian processes.

Author: Yongbo Peng

Publisher: Springer

ISBN: 9789811367649

Category: Technology & Engineering

Page: 322

View: 195

This book proposes, for the first time, a basic formulation for structural control that takes into account the stochastic dynamics induced by engineering excitations in the nature of non-stationary and non-Gaussian processes. Further, it establishes the theory of and methods for stochastic optimal control of randomly-excited engineering structures in the context of probability density evolution methods, such as physically-based stochastic optimal (PSO) control. By logically integrating randomness into control gain, the book helps readers design elegant control systems, mitigate risks in civil engineering structures, and avoid the dilemmas posed by the methods predominantly applied in current practice, such as deterministic control and classical linear quadratic Gaussian (LQG) control associated with nominal white noises.
Categories: Technology & Engineering

Perturbation Methods in Optimal Control

Perturbation Methods in Optimal Control

Describes, analyzes, and generalizes the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations.

Author: Alain Bensoussan

Publisher: Wiley

ISBN: 0471919942

Category: Mathematics

Page: 588

View: 140

Describes, analyzes, and generalizes the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations. Covers the most important theorems in deterministic and stochastic optimal control, the theory of ergodic control, and the use of control, including regular perturbations and singular perturbations.
Categories: Mathematics

General Pontryagin Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

General Pontryagin Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

Author: Qi Lü

Publisher: Springer

ISBN: 9783319066325

Category: Science

Page: 146

View: 372

The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.
Categories: Science