Mathematical Control Theory for Stochastic Partial Differential Equations

This book provides a comprehensive introduction to control theory for stochastic distributed parameter systems, a relatively new area of mathematical control theory. It discusses the new phenomena and challenges in studying controllability and optimal control problems, and introduces necessary mathematical tools such as the global Carleman estimate and the stochastic transposition method. The study of stochastic distributed parameter systems can provide insights into quantum control systems, and a basic understanding of functional analysis, partial differential equations, and control theory for deterministic systems is required.

Format: Paperback / softback
Length: 592 pages
Publication date: 18 September 2022
Publisher: Springer Nature Switzerland AG

This groundbreaking book is the first to systematically present control theory for stochastic distributed parameter systems, a relatively new branch of mathematical control theory. It delves into the intricate details of the new phenomena and challenges that arise in the study of controllability and optimal control problems for these systems. One of the key aspects of this field is the development of novel mathematical tools to address specific problems. For instance, the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations are crucial tools that have been developed to solve complex problems in this domain.

In a broader context, the stochastic distributed parameter control system stands as the most general control system within the realm of classical physics. By studying this field, researchers can gain valuable insights into quantum control systems as well. It is important to note that a solid foundation in functional analysis, partial differential equations, and control theory for deterministic systems is a prerequisite for understanding the concepts and theories presented in this book.

The book is organized into four chapters, each covering a different aspect of stochastic distributed parameter control systems. Chapter 1 provides an introduction to the topic, including a brief overview of stochastic processes and their applications in control theory. Chapter 2 focuses on the study of controllability, discussing the necessary conditions for a system to be controllable and the methods used to analyze controllability. Chapter 3 explores the concept of optimal control, discussing the principles of optimal control theory and the methods used to design optimal controllers for stochastic systems. Chapter 4 discusses the application of control theory to real-world systems, including examples from various fields such as finance, biology, and engineering.

Throughout the book, numerous examples and exercises are provided to illustrate the concepts and theories discussed. These examples help to reinforce the understanding of the material and provide practical insights into the application of control theory in real-world situations. Additionally, the book includes a comprehensive bibliography that provides further reading on the topic for those who wish to explore it in greater depth.

In conclusion, this groundbreaking book is a must-read for anyone interested in control theory for stochastic distributed parameter systems. It provides a comprehensive and up-to-date treatment of the topic, covering both the theoretical foundations and practical applications. With its clear and concise writing style, it is accessible to students and researchers alike, and it will undoubtedly serve as a valuable resource for years to come.

Weight: 920g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030823337
Edition number: 1st ed. 2021