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

by Jingrui Sun, Jiongmin Yong

Overview

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of shastic 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 shastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in shastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Product Details

ISBN-13:	9783030483050
Publisher:	Springer International Publishing
Publication date:	06/30/2020
Series:	SpringerBriefs in Mathematics
Edition description:	1st ed. 2020
Pages:	130
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Jingrui Sun received his PhD in Mathematics from the University of Science and Technology of China in 2015. From 2015 to 2017, he was a Postdoctoral Fellow at the Hong Kong Polytechnic University and then a Research Fellow at the National University of Singapore. From 2017 to 2018, he was a Visiting Assistant Professor at the University of Central Florida, USA. Since the spring of 2019, he has been an Assistant Professor at the Southern University of Science and Technology, China. Dr. Sun has broad interests in the area of control theory and its applications. Aside from his primary research on shastic optimal control and differential games, he is exploring forward and backward shastic differential equations, shastic analysis, and mathematical finance.

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 shastic control, shastic differential equations, and optimal control of partial differential equations. Professor Yong has co-authored the following influential books: “Shastic Control: Hamiltonian Systems and HJB Equations” (with X. Y. Zhou, Springer 1999), “Forward-Backward Shastic 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 shastic control problems.

Table of Contents

1.- Some Elements of Linear-Quadratic Optimal Controls.- 2. Linear-Quadratic Two-Person Differential Games.- 3. Mean-Field Linear-Quadratic Optimal Controls.