图书简介
This is a book on oTimal coTrol problems (OCPs) for paTial differeTial equTions (PDEs)ThT evolved from a series of coursesTaugT byThe aThors inThe laT few years T PolTecnico di Milano, bTh TThe undergraduTe and graduTe levels.The book coversThe whole range spanning fromThe sTup andThe rigorousTheorTical analysis of OCPs,The derivTion ofThe syTem of oTimalTy condTions,The proposTion of suTable numerical mThods,Their formulTion,Their analysis, includingTheir applicTionTo a broad sT of problems of praTical relevanceThe firT iTroduTory chaTer addresses a handful of represeTTive OCPs and preseTs an overview ofThe associTed mThemTical issues.The reT ofThe book is organized iToThree paTs: paT I provides preliminary conceTs of OCPs for algebraic and dynamical syTems; paT II addresses OCPs involving linear PDEs (moTly elliTic and parabolicType) and quadrTic coT funTions; paT III deals wTh more general classes of OCPsThT Tand behindThe advanced applicTions meTioned above.TaTing from simple problemsThT allow a “hands-on”TreTmeT,The reader is progressively ledTo a general framework suTableTo face a broader class of problems. Moreover,The inclusion of many pseudocodes allowsThe readerTo easily implemeTThe algorThms illuTrTedThroughoTTheTeTTheThree paTs ofThe book are suTableTo readers wTh variable mThemTical backgrounds, from advanced undergraduTeTo Ph.D. levels and beyond. We believeThT applied mThemTicians, compTTional scieTiTs, and engineers may findThis book useful for a conTruTive approachTowardThe solTion of OCPs inThe coTeT of complex applicTions.
1 IntrodCtion: Representative Examples, MathematCal StrCture.- Part I A Preview on Optimization andControl in Finite Dimensions.- 2 Prelude on Optimization: Finite Dimension SpCes.- 3 Algorithms for NumerCal Optimization.- 4 Prelude onControl: TheCase of AlgebraC and ODE Systems.- Part II Linear-QuadratC OptimalControl Problems.- 5 QuadratCControl problems governed by linear elliptC PDEs.- 6 NumerCal Approximation of Linear-QuadratC CPs.- 7 QuadratCControl Problems Governed by Linear Evolution PDEs.- 8 NumerCal Approximation of QuadratC CPs Governed by Linear Evolution PDEs.- Part III More general PDEConstrained optimization problems.- 9 A MathematCal Framework for Nonlinear CPs.- 10 AdvaCed SelCted ApplCations.- 11 Shape Optimization Problems.- Appendix A Toolbox of FuCtional Analysis.- Appendix B Toolbox of NumerCal Analysis.
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