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Mathematical Control Theory for Stochastic Partial Differential Equations: 101 (Probability Theory and Stochastic Modelling, 101) - Hardcover

Book 34 of 35: Probability Theory and Stochastic Modelling

Lü, Qi; Zhang, Xu

 
9783030823306: Mathematical Control Theory for Stochastic Partial Differential Equations: 101 (Probability Theory and Stochastic Modelling, 101)
Hardcover
ISBN 10: 303082330X ISBN 13: 9783030823306
Publisher: Springer, 2021

Synopsis

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.


"synopsis" may belong to another edition of this title.

About the Author

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 Systems & Control Letters.  His research interests include control theory for deterministic and stochastic partial differential equations and stochastic analysis.  

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.   

From the Back Cover

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.


"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2021
Language
English
ISBN 10 
303082330X
ISBN 13 
9783030823306
Binding
Hardcover
Edition number
1
Number of pages
605