Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems

Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems book. This book definitely worth reading, it is an incredibly well-written.

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems

Jingrui Sun,Jiongmin Yong
Stochastic Linear Quadratic Optimal Control Theory Differential Games and Mean Field Problems Book PDF

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 138 pages
File Size : 54,6 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030483067

Get Book

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions

Jingrui Sun,Jiongmin Yong
Stochastic Linear Quadratic Optimal Control Theory Open Loop and Closed Loop Solutions Book PDF

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 129 pages
File Size : 41,7 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030209223

Get Book

Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications

Rene Carmona
Lectures on BSDEs Stochastic Control and Stochastic Differential Games with Financial Applications Book PDF

Author : Rene Carmona
Publisher : SIAM
Page : 265 pages
File Size : 53,9 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974249

Get Book

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by Rene Carmona Pdf

The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.

Mean Field Games and Mean Field Type Control Theory

Alain Bensoussan,Jens Frehse,Phillip Yam
Mean Field Games and Mean Field Type Control Theory Book PDF

Author : Alain Bensoussan,Jens Frehse,Phillip Yam
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 46,5 Mb
Release : 2013-10-16
Category : Science
ISBN : 9781461485087

Get Book

Mean Field Games and Mean Field Type Control Theory by Alain Bensoussan,Jens Frehse,Phillip Yam Pdf

​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. ​

Modeling, Stochastic Control, Optimization, and Applications

George Yin,Qing Zhang
Modeling Stochastic Control Optimization and Applications Book PDF

Author : George Yin,Qing Zhang
Publisher : Springer
Page : 599 pages
File Size : 54,9 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9783030254988

Get Book

Modeling, Stochastic Control, Optimization, and Applications by George Yin,Qing Zhang Pdf

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Matrix Riccati Equations in Control and Systems Theory

Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank
Matrix Riccati Equations in Control and Systems Theory Book PDF

Author : Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank
Publisher : Birkhäuser
Page : 584 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034880817

Get Book

Matrix Riccati Equations in Control and Systems Theory by Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank Pdf

The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

Mean-Field-Type Games for Engineers

JULIAN. TEMBINE BARREIRO-GOMEZ (HAMIDOU.),Hamidou Tembine
Mean Field Type Games for Engineers Book PDF

Author : JULIAN. TEMBINE BARREIRO-GOMEZ (HAMIDOU.),Hamidou Tembine
Publisher : CRC Press
Page : 528 pages
File Size : 42,5 Mb
Release : 2021-11-24
Category : Electronic
ISBN : 0367566125

Get Book

Mean-Field-Type Games for Engineers by JULIAN. TEMBINE BARREIRO-GOMEZ (HAMIDOU.),Hamidou Tembine Pdf

This book comprises an appropriate background to work and do research on mean-field-type control and game theory. It starts with studying the deterministic optimal control and differential linear-quadratic games, and progressively moves to analyzing mean-field-type control and game problems incorporating several stochastic processes.

LQ Dynamic Optimization and Differential Games

Jacob Engwerda
LQ Dynamic Optimization and Differential Games Book PDF

Author : Jacob Engwerda
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 55,7 Mb
Release : 2005-06-17
Category : Business & Economics
ISBN : 0470015241

Get Book

LQ Dynamic Optimization and Differential Games by Jacob Engwerda Pdf

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.

Advances in Dynamic and Mean Field Games

Joseph Apaloo,Bruno Viscolani
Advances in Dynamic and Mean Field Games Book PDF

Author : Joseph Apaloo,Bruno Viscolani
Publisher : Birkhäuser
Page : 363 pages
File Size : 46,6 Mb
Release : 2018-01-03
Category : Mathematics
ISBN : 9783319706191

Get Book

Advances in Dynamic and Mean Field Games by Joseph Apaloo,Bruno Viscolani Pdf

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and graduate students.

Essays on Pareto Optimality in Cooperative Games

Yaning Lin,Weihai Zhang
Essays on Pareto Optimality in Cooperative Games Book PDF

Author : Yaning Lin,Weihai Zhang
Publisher : Springer Nature
Page : 169 pages
File Size : 43,5 Mb
Release : 2022-09-21
Category : Technology & Engineering
ISBN : 9789811950490

Get Book

Essays on Pareto Optimality in Cooperative Games by Yaning Lin,Weihai Zhang Pdf

The book focuses on Pareto optimality in cooperative games. Most of the existing works focus on the Pareto optimality of deterministic continuous-time systems or for the regular convex LQ case. To expand on the available literature, we explore the existence conditions of Pareto solutions in stochastic differential game for more general cases. In addition, the LQ Pareto game for stochastic singular systems, Pareto-based guaranteed cost control for uncertain mean-field stochastic systems, and the existence conditions of Pareto solutions in cooperative difference game are also studied in detail. Addressing Pareto optimality for more general cases and wider systems is one of the major features of the book, making it particularly suitable for readers who are interested in multi-objective optimal control. Accordingly, it offers a valuable asset for researchers, engineers, and graduate students in the fields of control theory and control engineering, economics, management science, mathematics, etc.

Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems

Valery Y. Glizer,Oleg Kelis
Singular Linear Quadratic Zero Sum Differential Games and H Control Problems Book PDF

Author : Valery Y. Glizer,Oleg Kelis
Publisher : Springer Nature
Page : 211 pages
File Size : 44,9 Mb
Release : 2022-08-29
Category : Mathematics
ISBN : 9783031070518

Get Book

Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems by Valery Y. Glizer,Oleg Kelis Pdf

This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors’ previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections. Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area

Game Theory

Danijela Tuljak-Suban
Game Theory Book PDF

Author : Danijela Tuljak-Suban
Publisher : BoD – Books on Demand
Page : 132 pages
File Size : 40,8 Mb
Release : 2018-09-26
Category : Mathematics
ISBN : 9781789238976

Get Book

Game Theory by Danijela Tuljak-Suban Pdf

This book provides a wide range of examples of the uses of game theory, even in situations where such application may seem unsuitable. This book explores cooperative, competitive, leader-follower games and the free-rider problem - as well as games with the aim of maintaining friendships or team work. The reader will be presented with a wide range of practical applications of game theory.

Stochastic Analysis and Applications

Fred Espen Benth,Giulia Di Nunno,Tom Lindstrom,Bernt Øksendal,Tusheng Zhang
Stochastic Analysis and Applications Book PDF

Author : Fred Espen Benth,Giulia Di Nunno,Tom Lindstrom,Bernt Øksendal,Tusheng Zhang
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 45,9 Mb
Release : 2007-04-24
Category : Mathematics
ISBN : 9783540708476

Get Book

Stochastic Analysis and Applications by Fred Espen Benth,Giulia Di Nunno,Tom Lindstrom,Bernt Øksendal,Tusheng Zhang Pdf

The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over presented the newest developments within the exciting and fast growing field of stochastic analysis. This volume combines both papers from the invited speakers and contributions by the presenting lecturers. In addition, it includes the Memoirs that Kiyoshi Ito wrote for this occasion.

Stochastic and Differential Games

Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Stochastic and Differential Games Book PDF

Author : Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215929

Get Book

Stochastic and Differential Games by Martino Bardi,T.E.S. Raghavan,T. Parthasarathy Pdf

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.

Mean-Field-Type Games for Engineers

Julian Barreiro-Gomez,Hamidou Tembine
Mean Field Type Games for Engineers Book PDF

Author : Julian Barreiro-Gomez,Hamidou Tembine
Publisher : CRC Press
Page : 526 pages
File Size : 43,8 Mb
Release : 2021-11-18
Category : Technology & Engineering
ISBN : 9781000473537

Get Book

Mean-Field-Type Games for Engineers by Julian Barreiro-Gomez,Hamidou Tembine Pdf

The contents of this book comprise an appropriate background to start working and doing research on mean-field-type control and game theory. To make the exposition and explanation even easier, we first study the deterministic optimal control and differential linear-quadratic games. Then, we progressively add complexity step-by-step and little-by-little to the problem settings until we finally study and analyze mean-field-type control and game problems incorporating several stochastic processes, e.g., Brownian motions, Poisson jumps, and random coefficients. We go beyond the Nash equilibrium, which provides a solution for non- cooperative games, by analyzing other game-theoretical concepts such as the Berge, Stackelberg, adversarial/robust, and co-opetitive equilibria. For the mean-field-type game analysis, we provide several numerical examples using a Matlab-based user-friendly toolbox that is available for the free use to the readers of this book. We present several engineering applications in both continuous and discrete time. Among these applications we find the following: water distribution systems, micro-grid energy storage, stirred tank reactor, mechanism design for evolutionary dynamics, multi-level building evacuation problem, and the COVID-19 propagation control. Julian Barreiro-Gomez Hamidou Tembine With such a demand from engineering audiences, this book is very timely and provides a thorough study of mean-field-type game theory. The strenuous protagonist of this book is to bridge between the theoretical findings and engineering solutions. The book introduces the basics first, and then mathematical frameworks are elaborately explained. The engineering application examples are shown in detail, and the popular learning approaches are also investigated. Those advantageous characteristics will make this book a comprehensive handbook of many engineering fields for many years, and I will buy one when it gets published. Zhu Han