Overview
- Provides a detailed overview of stochastic linear-quadratic control theory
- Largely self-contained, allowing readers to pursue independent study
- Includes several explicitly worked-out examples, helping readers to easily understand the theory discussed
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (3 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the authors
Jiongmin Yong received his PhD from Purdue University in 1986 and is currently a Professor of Mathematics at the University of Central Florida, USA. His main research interests include stochastic control, stochastic differential equations, and optimal control of partial differential equations. Professor Yong has co-authored the following influential books: “Stochastic Control: Hamiltonian Systems and HJB Equations” (with X. Y. Zhou, Springer 1999), “Forward-Backward Stochastic Differential Equations and Their Applications” (with J. Ma, Springer 1999), and “Optimal Control Theory for Infinite-Dimensional Systems” (with X. Li, Birkhauser 1995). His current interests include time-inconsistent stochastic control problems.
Bibliographic Information
Book Title: Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems
Authors: Jingrui Sun, Jiongmin Yong
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-48306-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-48305-0Published: 30 June 2020
eBook ISBN: 978-3-030-48306-7Published: 29 June 2020
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XII, 130
Number of Illustrations: 1 illustrations in colour
Topics: Optimization, Probability Theory and Stochastic Processes, Systems Theory, Control, Philosophy of Mathematics