Numerical Methods for Optimal Control Problems with SPDEs

Andreas Prohl, Yanqing Wang (Autoren)

Buch | Softcover

133 Seiten

2026
Springer Verlag, Singapore
978-981-95-4468-4 (ISBN)

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This book is on the construction and convergence analysis of implementable algorithms to approximate the optimal control of a stochastic linear-quadratic optimal control problem (SLQ problem, for short) subject to a stochastic PDE. If compared to finite dimensional stochastic control theory, the increased complexity due to high-dimensionality requires new numerical concepts to approximate SLQ problems; likewise, well-established discretization and numerical optimization strategies from infinite dimensional deterministic control theory need fundamental changes to properly address the optimality system, where to approximate the solution of a backward stochastic PDE is conceptually new. The linear-quadratic structure of SLQ problems allows two equivalent analytical approaches to characterize its minimum: ‘open loop’ is based on Pontryagin’s maximum principle, and ‘closed loop’ utilizes the stochastic Riccati equation in combination with the feedback control law. The authors will discuss why, in general, complexities of related numerical schemes differ drastically, and when which direction should be given preference from an algorithmic viewpoint.

Andreas Prohl is a professor at Eberhard Karls Universität Tübingen in Germany. Yanqing Wang is currently an Associate Professor in the School of Mathematics and Statistics at Southwest University, Chongqing, China. His research interests include numerics of stochastic optimal control and the controllability of linear stochastic systems.

Introduction.- Preliminaries.- Discretization based on the open-loop approach.- Discretization based on the closed-loop approach.

Erscheinungsdatum	29.11.2025
Reihe/Serie	SpringerBriefs on PDEs and Data Science
Zusatzinfo	7 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	error analysis with rates • linear-quadratic stochastic control problem • Numerical analysis • optimal control with stochastic PDEs • Pontryagin Maximum Principle • stochastic Riccati equation
ISBN-10	981-95-4468-8 / 9819544688
ISBN-13	978-981-95-4468-4 / 9789819544684
Zustand	Neuware