Mathematical control theory for stochastic partial differential equations
Lu, Qi
Mathematical control theory for stochastic partial differential equations - Cham : Springer, 2021. - xiii, 592 pages - Probability theory and stochastic modelling, volume 101 2199-3130 ; .
Includes bibliographical references and 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.
9783030823306
Stochastic control theory
Stochastic differential equations
Distributed parameter systems
Stochastic stability in control theory
Stochastic evolution equation
519.21 / LU-M
Mathematical control theory for stochastic partial differential equations - Cham : Springer, 2021. - xiii, 592 pages - Probability theory and stochastic modelling, volume 101 2199-3130 ; .
Includes bibliographical references and 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.
9783030823306
Stochastic control theory
Stochastic differential equations
Distributed parameter systems
Stochastic stability in control theory
Stochastic evolution equation
519.21 / LU-M
