Mathematical control theory for stochastic partial differential equations / Qi Lü, Xu Zhang.
Lü, Qi, author.; Zhang, Xu, author.
2021
QA402.37 .L8 2021
Available Online

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Title
Mathematical control theory for stochastic partial differential equations / Qi Lü, Xu Zhang.
Author
Lü, Qi, author.
ISBN
9783030823313 (electronic bk.)
3030823318 (electronic bk.)
9783030823306
303082330X
DOI
https://doi.org/10.1007/978-3-030-82331-3
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-82331-3 doi
Call Number
QA402.37 .L8 2021
Dewey Decimal Classification
003/.76
Summary
This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed September 27, 2021).
Added Author
Zhang, Xu, author.
Series
Probability theory and stochastic modelling ; v. 101. 2199-3149
Available in Other Form
Print version: 9783030823306
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1 Introduction
2 Some Preliminaries in Stochastic Calculus
3 Stochastic Evolution Equations
4 Backward Stochastic Evolution Equations
5 Control Problems in Stochastic Distributed Parameter Systems
6 Controllability for Stochastic Differential Equations in Finite Dimensions
7 Controllability for Stochastic Linear Evolution Equations
8 Exact Controllability for Stochastic Transport Equations
9 Controllability and Observability of Stochastic Parabolic Systems
10 Exact Controllability for a Refined Stochastic Wave Equation
11 Exact Controllability for Stochastic Schrödinger Equations
12 Pontryagin-Type Stochastic Maximum Principle
13 Linear Quadratic Optimal Control Problems
References
Index.

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