Mathematical Control Theory for Stochastic Partial Differential Equations

Xu Zhang

ISBN 10: 3030823334 / ISBN 13: 9783030823337

Editore: Springer International Publishing, 2022

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783030823337

Dati bibliografici

• Titolo: Mathematical Control Theory for Stochastic Partial Differential Equations
• Editore: Springer International Publishing
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 3030823334
• ISBN 13: 9783030823337
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 33 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 33 millimetri di profondità
• Peso: 908 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.