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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Optimal Control of Partial Differential Equations - Analysis, Approximation, and Applications (Hardcover, 1st ed. 2021)
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Optimal Control of Partial Differential Equations - Analysis, Approximation, and Applications (Hardcover, 1st ed. 2021)
Series: Applied Mathematical Sciences, 207
Expected to ship within 10 - 15 working days
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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 of OCPs 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.
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