Details

Mathematical Control Theory for Stochastic Partial Differential Equations


Mathematical Control Theory for Stochastic Partial Differential Equations


Probability Theory and Stochastic Modelling, Band 101

von: Qi Lü, Xu Zhang

CHF 177.00

Verlag: Springer
Format: PDF
Veröffentl.: 17.09.2021
ISBN/EAN: 9783030823313
Sprache: englisch

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

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.<div><br></div><div>A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.<p></p><p><br></p></div>
1 Introduction.-&nbsp;2 Some Preliminaries in Stochastic Calculus.-&nbsp;3 Stochastic Evolution Equations.-&nbsp;4 Backward Stochastic Evolution Equations.-&nbsp;5 Control Problems in Stochastic Distributed Parameter&nbsp;Systems.-&nbsp;6 Controllability for Stochastic Differential Equations in Finite Dimensions.- 7 Controllability for Stochastic Linear Evolution Equations.-&nbsp;8 Exact Controllability for Stochastic Transport Equations<i>.-&nbsp;</i>9 Controllability and Observability of Stochastic Parabolic&nbsp;Systems<i>.-&nbsp;</i>10 Exact Controllability for a Refined Stochastic Wave Equation<i>.-&nbsp;</i>11 Exact Controllability for Stochastic Schrödinger&nbsp;Equations.-&nbsp;12 Pontryagin-Type Stochastic Maximum Principle.-&nbsp;13 Linear Quadratic Optimal Control Problems.-&nbsp;References.-&nbsp;Index.
<p>Qi Lü is a professor at School of Mathematics, Sichuan University, Chengdu, China. He is currently an associate editor/editorial board member of several journals including <i>Systems & Control Letters</i>. &nbsp;His research interests include control theory for deterministic and stochastic partial differential equations and stochastic analysis. &nbsp;</p>

<p>Xu Zhang is a Cheung Kong Scholar Distinguished Professor at School of Mathematics, Sichuan University, Chengdu, China. He is a sectional speaker at International Congress of Mathematicians (Control Theory & Optimization Section, 2010). He is/was the editor in chief/corresponding editor/associate editor for several journals including Mathematical Control and Related Fields, ESAIM: Control, Optimisation and Calculus of Variations, and SIAM Journal on Control and Optimization. His research interests include control theory, partial differential equations and stochastic analysis.&nbsp; &nbsp;<br></p>
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.<div><br></div><div>A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.<p></p><p><br></p></div>
Control theory for stochastic distributed parameters is a new branch New tools presented in this book Required reading for anyone who wants to study quantum control systems mathematically

Diese Produkte könnten Sie auch interessieren:

Marginal Models
Marginal Models
von: Wicher Bergsma, Marcel A. Croon, Jacques A. Hagenaars
PDF ebook
CHF 118.00
Reactive Search and Intelligent Optimization
Reactive Search and Intelligent Optimization
von: Roberto Battiti, Mauro Brunato, Franco Mascia
PDF ebook
CHF 118.00