Overview
- Offers a strong interplay between theory, numerics & applications
- Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework, suitable to face a broader class of problems
- Multi-layered presentation: the book is split into three parts that are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and above
Part of the book series: Applied Mathematical Sciences (AMS, volume 207)
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Table of contents (11 chapters)
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Front Matter
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A Preview on Optimization and Control in Finite Dimensions
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Front Matter
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Linear-Quadratic Optimal Control Problems
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Front Matter
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More General PDE-Constrained Optimization Problems
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Front Matter
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Back Matter
Keywords
About this book
This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance.
The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes ofOCPs that stand behind the advanced applications mentioned above.Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text.
The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Reviews
Authors and Affiliations
About the authors
Andrea Manzoni, PhD, is an Associate Professor of Numerical Analysis at Politecnico of Milan. He is the author of 2 books and of approximately 50 papers. In 2012 he won the ECCOMAS Award for the best PhD thesis in Europe about Computational Methods in Applied Sciences and Engineering and the Biannual SIMAI prize (Italian Society of Applied and Industrial Mathematics) in 2017. His research interests include the development of reduced-order modelling techniques for PDEs, PDE-constrained optimization, uncertainty quantification, computational statistics, and machine/deep learning.
Alfio Quarteroni is a Professor of Numerical Analysis at Politecnico of Milan and Professor Emeritus at EPFL, Lausanne. He is the author of 25 books, editor of 12 books, author of about 400 papers. He is the recipient of two ERC Advanced Grants. He is a member of the Italian Academy of Science, the European Academy of Science, Academia Europaea, and the Lisbon Academy of Science. His research Group at EPFL has carried out the mathematical simulation for the Alinghi sailing boat, the winner of two editions (2003 and 2007) of America’s Cup. His research interests include mathematical modeling and its applications at large.
Sandro Salsa is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on free boundary problems. He is an author of 13 books and several papers in the most prestigious scientific mathematical journals.
Bibliographic Information
Book Title: Optimal Control of Partial Differential Equations
Book Subtitle: Analysis, Approximation, and Applications
Authors: Andrea Manzoni, Alfio Quarteroni, Sandro Salsa
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-030-77226-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-77225-3Published: 11 December 2021
Softcover ISBN: 978-3-030-77228-4Published: 11 December 2022
eBook ISBN: 978-3-030-77226-0Published: 01 January 2022
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XVII, 498
Number of Illustrations: 24 b/w illustrations, 59 illustrations in colour
Topics: Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations, Computational Mathematics and Numerical Analysis, Mathematical and Computational Engineering, Numerical and Computational Physics, Simulation