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.
