Infinite Horizon Optimal Control
Infinite Horizon Optimal Control

Author: Dean A. Carlson

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 270

ISBN-13: 3662025299

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This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. 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", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a 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 famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.

Optimal Control Theory with Applications in Economics
Optimal Control Theory with Applications in Economics

Author: Thomas A. Weber

Publisher: MIT Press

Published: 2011-09-30

Total Pages: 387

ISBN-13: 0262015730

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A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

Turnpike Phenomenon and Infinite Horizon Optimal Control
Turnpike Phenomenon and Infinite Horizon Optimal Control

Author: Alexander J. Zaslavski

Publisher: Springer

Published: 2014-09-04

Total Pages: 377

ISBN-13: 3319088289

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This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value integrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Researchers in other fields such as economics and game theory, where turnpike properties are well known, will also find this Work valuable.

Intelligent Autonomous Systems 17
Intelligent Autonomous Systems 17

Author: Ivan Petrovic

Publisher: Springer Nature

Published: 2023-01-17

Total Pages: 941

ISBN-13: 3031222164

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“IAS has been held every two years since 1986 providing venue for the latest accomplishments and innovations in advanced intelligent autonomous systems. New technologies and application domains continuously pose new challenges to be overcome in order to apply intelligent autonomous systems in a reliable and user-independent way in areas ranging from industrial applications to professional service and household domains. The present book contains the papers presented at the 17th International Conference on Intelligent Autonomous Systems (IAS-17), which was held from June 13–16, 2022, in Zagreb, Croatia. In our view, 62 papers, authored by 196 authors from 19 countries, are a testimony to the appeal of the conference considering travel restrictions imposed by the COVID-19 pandemic. Our special thanks go to the authors and the reviewers for their effort—the results of their joint work are visible in this book. We look forward to seeing you at IAS-18 in 2023 in Suwon, South Korea!”

Stochastic Optimal Control in Infinite Dimension
Stochastic Optimal Control in Infinite Dimension

Author: Giorgio Fabbri

Publisher: Springer

Published: 2017-06-22

Total Pages: 928

ISBN-13: 3319530674

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Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Variational and Optimal Control Problems on Unbounded Domains
Variational and Optimal Control Problems on Unbounded Domains

Author: Gershon Wolansky

Publisher: American Mathematical Soc.

Published: 2014-07-01

Total Pages: 266

ISBN-13: 147041077X

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This volume contains the proceedings of the workshop on Variational and Optimal Control Problems on Unbounded Domains, held in memory of Arie Leizarowitz, from January 9-12, 2012, in Haifa, Israel. The workshop brought together a select group of worldwide experts in optimal control theory and the calculus of variations, working on problems on unbounded domains. The papers in this volume cover many different areas of optimal control and its applications. Topics include needle variations in infinite-horizon optimal control, Lyapunov stability with some extensions, small noise large time asymptotics for the normalized Feynman-Kac semigroup, linear-quadratic optimal control problems with state delays, time-optimal control of wafer stage positioning, second order optimality conditions in optimal control, state and time transformations of infinite horizon problems, turnpike properties of dynamic zero-sum games, and an infinite-horizon variational problem on an infinite strip. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

Analysis and Design of Networked Control Systems under Attacks
Analysis and Design of Networked Control Systems under Attacks

Author: Yuan Yuan

Publisher: CRC Press

Published: 2018-09-21

Total Pages: 219

ISBN-13: 0429812272

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This book adopts a systematic view of the control systems in cyber-physical systems including the security control of the optimal control system, security control of the non-cooperative game system, quantify the impact of the Denial-of-Service attacks on the optimal control system, and the adaptive security control of the networked control systems. Because the cyber-physical system is a hybrid system, it adopts cross layer approach to handle the security control of the CPS. It presents a number of attack models according to the attack scenario and defense facilities, and a number of cross-layer co-design methodologies to secure the control of CPS.

Control of Partial Differential Equations
Control of Partial Differential Equations

Author: Giuseppe Da Prato

Publisher: CRC Press

Published: 1994-08-19

Total Pages: 296

ISBN-13: 1482277654

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This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.

Topics in Control and its Applications
Topics in Control and its Applications

Author: Daniel E. Miller

Publisher: Springer Science & Business Media

Published: 1999

Total Pages: 232

ISBN-13: 9781852331504

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This book comprises the proceedings of the Recent Developments in Control Theory and Applications workshop held in Toronto, Canada, 29th-30th June 1998 in honor of the 60th birthday of E.J. Davison. While the scope of the workshop was quite broad, the main theme was robust control, decentralized control and applications. Some topics include: - robust control for car steering - flow control for networks - fault diagnosis in discrete event systems. With contributions from distinguished authors of international repute, the material presented here focuses upon new findings in the field of control including interesting applications. As well as being informative, it is a useful tool for practitioners of systems and control to ascertain new developments in the field.