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Mathematical control theory for stoc...

Lu, Qi.

Mathematical control theory for stochastic partial differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mathematical control theory for stochastic partial differential equationsby Qi Lu, Xu Zhang.
作者:	Lu, Qi.
其他作者:	Zhang, Xu.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xiii, 592 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Stochastic control theory.
電子資源:	https://doi.org/10.1007/978-3-030-82331-3
ISBN:	9783030823313$q(electronic bk.)

Mathematical control theory for stochastic partial differential equations
Lu, Qi.

Mathematical control theory for stochastic partial differential equations[electronic resource] /by Qi Lu, Xu Zhang. - Cham :Springer International Publishing :2021. - xiii, 592 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.1012199-3149 ;. - Probability theory and stochastic modelling ;v.70..

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 Schrodinger Equations -- 12 Pontryagin-Type Stochastic Maximum Principle -- 13 Linear Quadratic Optimal Control Problems -- References -- Index.

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.

ISBN: 9783030823313$q(electronic bk.)

Standard No.: 10.1007/978-3-030-82331-3doiSubjects--Topical Terms:

183121
Stochastic control theory.

LC Class. No.: QA402.37 / .L8 2021

Dewey Class. No.: 003.76

Mathematical control theory for stochastic partial differential equations
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505 0 $a 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 Schrodinger Equations -- 12 Pontryagin-Type Stochastic Maximum Principle -- 13 Linear Quadratic Optimal Control Problems -- References -- Index.
520 $a 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.
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