Optimal Control And Differential Games
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| Author | : Alexander Tarasyev |
| Publisher | : Springer Nature |
| Total Pages | : 380 |
| Release | : 2020-05-29 |
| Genre | : Technology & Engineering |
| ISBN | : 3030428311 |
This book presents the proceedings of the International Conference “Stability, Control, Differential Games” (SCDG2019, September 16 – 20, 2019, Yekaterinburg, Russia), organized by the Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. Discussing the latest advances in the theory of optimal control, stability theory and differential games, it also demonstrates the application of new techniques and numerical algorithms to solve problems in robotics, mechatronics, power and energy systems, economics and ecology. Further, the book includes fundamental results in control theory, stability theory and differential games presented at the conference, as well as a number of chapters focusing on novel approaches in solving important applied problems in control and optimization. Lastly, it evaluates recent major accomplishments, and forecasts developments in various up-and-coming areas, such as hybrid systems, model predictive control, Hamilton–Jacobi equations and advanced estimation algorithms.
| Author | : Draguna L. Vrabie |
| Publisher | : IET |
| Total Pages | : 305 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 1849194890 |
The book reviews developments in the following fields: optimal adaptive control; online differential games; reinforcement learning principles; and dynamic feedback control systems.
| Author | : Martino Bardi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 1999-06 |
| Genre | : Mathematics |
| ISBN | : 9780817640293 |
The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.
| Author | : Suresh P. Sethi |
| Publisher | : Taylor & Francis US |
| Total Pages | : 536 |
| Release | : 2006 |
| Genre | : Business & Economics |
| ISBN | : 9780387280929 |
Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.
| Author | : Jacob Engwerda |
| Publisher | : John Wiley & Sons |
| Total Pages | : 514 |
| Release | : 2005-06-17 |
| Genre | : Business & Economics |
| ISBN | : 9780470015247 |
Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.
| Author | : Tamer Başar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 417 |
| Release | : 2009-05-21 |
| Genre | : Science |
| ISBN | : 0817647570 |
This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. The book can be used for a second or third year graduate level course in the subject, and researchers working in the area will find the book useful as a standard reference. Based mostly on recent work of the authors, the book is written on a good mathematical level. Many results in it are original, interesting, and inspirational. The topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with important theoretical developments in applied mathematics and control.
| Author | : Georges Zaccour |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 242 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 1461510473 |
Optimal control and differential games continue to attract strong interest from researchers interested in dynamical problems and models in management science. This volume explores the application of these methodologies to new as well as to classical decision problems in management sciences and economics. In Part I, optimal control and dynamical systems approaches are used to analyze problems in areas such as monetary policy, pollution control, relationship marketing, drug control, debt financing, and ethical behavior. In Part II differential games are applied to problems such as oligopolistic competition, common resource management, spillovers in foreign direct investments, marketing channels, incentive strategies, and the computation of Markov perfect Nash equilibria. Optimal Control and Differential Games is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in management science.
| Author | : Terry L. Friesz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 509 |
| Release | : 2010-08-20 |
| Genre | : Business & Economics |
| ISBN | : 0387727787 |
This book has been written to address the increasing number of Operations Research and Management Science problems (that is, applications) that involve the explicit consideration of time and of gaming among multiple agents. It is a book that will be used both as a textbook and as a reference and guide by those whose work involves the theoretical aspects of dynamic optimization and differential games.
| Author | : Morton I. Kamien |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 0486310280 |
Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
| Author | : Thomas A. Weber |
| Publisher | : MIT Press |
| Total Pages | : 387 |
| Release | : 2011-09-30 |
| Genre | : Business & Economics |
| ISBN | : 0262015730 |
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.
