calculus of variations & optimal control - sasane

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1、CalculusofVariationsandOptimalControliiiPrefaceThispamphletoncalculusofvariationsandoptimalcontroltheorycontainsthemostimpor-tantresultsinthesubject,treatedlargelyinorderofurgency.Familiaritywithlinearalgebraandrealanalysisareassumed.Itisdesirable,althoughnotmandatory,thatt

2、hereaderhasalsohadacourseondifferentialequations.Iwouldgreatlyappreciatereceivinginformationaboutanyerrorsnoticedbythereaders.IamthankfultoDr.SaraMaadfromtheUniversityofVirginia,U.S.A.,forseveralusefuldiscussions.AmolSasane6September,2004.CoursedescriptionofMA305:ControlTheo

3、ryLecturer:Dr.AmolSasaneOverviewThisahighlevelmethodscoursecentredontheestablishmentofacalculusappropriatetooptimisationproblemsinwhichthevariablequantityisafunctionorcurve.Suchacurvemightdescribetheevolutionovercontinuoustimeofthestateofadynamicalsystem.Thisistypicalofmode

4、lsofconsumptionorproductionineconomicsandfinancialmathematics(andformodelsinmanyotherdisciplinessuchasengineeringandphysics).Theemphasisofthecourseisoncalculations,butthereisalsosometheory.AimsTheaimofthiscourseistointroducestudentstothetypesofproblemsencounteredinoptimalco

5、ntrol,toprovidetechniquestoanalyseandsolvetheseproblems,andtoprovideexamplesofwherethesetechniquesareusedinpractice.LearningOutcomesAfterhavingfollowedthiscourse,studentsshould*haveknowledgeandunderstandingofimportantdefinitions,conceptsandresults,andhowtoapplytheseindiffer

6、entsituations;*haveknowledgeofbasictechniquesandmethodologiesinthetopicscoveredbelow;*haveabasicunderstandingofthetheoreticalaspectsoftheconceptsandmethodologiescovered;*beabletounderstandnewsituationsanddefinitions;*beabletothinkcriticallyandwithsufficientmathematicalrigou

7、r;*beabletoexpressargumentsclearlyandprecisely.Thecoursewillcoverthefollowingcontent:1.ExamplesofOptimalControlProblems.2.NormedLinearSpacesandCalculusofVariations.3.Euler-LagrangeEquation.4.OptimalControlProblemswithUnconstrainedControls.5.TheHamiltonianandPontryaginMinimu

8、mPrinciple.6.Constraintonthestateatfinaltime.Controllability.7.OptimalityPrinciple