TY  - GEN
AB  - 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.
AU  - Lü, Qi,
AU  - Zhang, Xu,
CN  - QA402.37
DO  - 10.1007/978-3-030-82331-3
DO  - doi
ID  - 1439770
KW  - Stochastic control theory.
KW  - Stochastic differential equations.
KW  - Distributed parameter systems.
KW  - Commande stochastique.
KW  - Équations différentielles stochastiques.
KW  - Systèmes à paramètres répartis.
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-82331-3
N2  - 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.
SN  - 9783030823313
SN  - 3030823318
T1  - Mathematical control theory for stochastic partial differential equations /
TI  - Mathematical control theory for stochastic partial differential equations /
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-82331-3
VL  - volume 101
ER  -