calculus of variations & optimal control - sasane

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1、CalculusofVariationsandOptimalControliiiPrefaceThispamphletoncalculusofvariationsandoptimalcontroltheorycontainsthemostimpor-tantresultsinthesubject,treatedlargelyinorderofurgency.Familiaritywithlinearalgebraandrealanalysisareassumed.Itisdesirable,althoughnotma

2、ndatory,thatthereaderhasalsohadacourseondifferentialequations.Iwouldgreatlyappreciatereceivinginformationaboutanyerrorsnoticedbythereaders.IamthankfultoDr.SaraMaadfromtheUniversityofVirginia,U.S.A.,forseveralusefuldiscussions.AmolSasane6September,2004.Coursedesc

3、riptionofMA305:ControlTheoryLecturer:Dr.AmolSasaneOverviewThisahighlevelmethodscoursecentredontheestablishmentofacalculusappropriatetooptimisationproblemsinwhichthevariablequantityisafunctionorcurve.Suchacurvemightdescribetheevolutionovercontinuoustimeofthestat

4、eofadynamicalsystem.Thisistypicalofmodelsofconsumptionorproductionineconomicsandfinancialmathematics(andformodelsinmanyotherdisciplinessuchasengineeringandphysics).Theemphasisofthecourseisoncalculations,butthereisalsosometheory.AimsTheaimofthiscourseistointrodu

5、cestudentstothetypesofproblemsencounteredinoptimalcontrol,toprovidetechniquestoanalyseandsolvetheseproblems,andtoprovideexamplesofwherethesetechniquesareusedinpractice.LearningOutcomesAfterhavingfollowedthiscourse,studentsshould*haveknowledgeandunderstandingofi

6、mportantdefinitions,conceptsandresults,andhowtoapplytheseindifferentsituations;*haveknowledgeofbasictechniquesandmethodologiesinthetopicscoveredbelow;*haveabasicunderstandingofthetheoreticalaspectsoftheconceptsandmethodologiescovered;*beabletounderstandnewsitua

7、tionsanddefinitions;*beabletothinkcriticallyandwithsufficientmathematicalrigour;*beabletoexpressargumentsclearlyandprecisely.Thecoursewillcoverthefollowingcontent:1.ExamplesofOptimalControlProblems.2.NormedLinearSpacesandCalculusofVariations.3.Euler-LagrangeEqu

8、ation.4.OptimalControlProblemswithUnconstrainedControls.5.TheHamiltonianandPontryaginMinimumPrinciple.6.Constraintonthestateatfinaltime.Controllability.7.OptimalityPrinciple