Mathematical Control Theory for Stochastic Partial Differential Equations
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
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
Autor*in
Qi Lü
Themen in »Mathematical Control Theory for Stochastic Partial Differential Equations«
stochastic evolution equation control theory controllability observability optimal control global Carleman estimate stochastic transposition method
Stimmen zu »Mathematical Control Theory for Stochastic Partial Differential Equations«
“This book of about 600 pages presents in an appealing manner how control theory can be applied for stochastic partial differential equations. I recommend it to all students and researchers interested in these topics.” (Gheorghe Tigan, zbMATH 1497.93001, 2022)
()