what is optimal control theory

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1、Chapter1WhatisOptimalControlTheory?Manymanagementscienceapplicationsinvolvethecontrolofdynamicsystems,i.e.,systemsthatevolveovertime.Theyarecalledcontinuous-timesystemsordiscrete-timesystemsdependingonwhethertimevariescontinuouslyordiscretely.Weshalldealwithbothkindsofsystemsinthisbook,altho

2、ughthemainemphasiswillbeoncontinuous-timesystems.Optimalcontroltheoryisabranchofmathematicsdevelopedtofindoptimalwaystocontroladynamicsystem.Thepurposeofthisbookistogiveanelementaryintroductiontomathematicaltheoryandthentoapplyittoawidevarietyofdifferentsituationsarisinginmanagementscience.W

3、ehavedeliberatelykeptthelevelofmathematicsassimpleaspossibleinordertomakethebookaccessibletoalargeaudience.Theonlymathematicalrequirementsforthisbookareelementarycalculus,includingpartialdifferentiation,someknowledgeofvectorsandmatrices,andelementaryordinaryandpartialdifferentialequations.Mo

4、reover,thelasttopicisbrieflycoveredinAppendixA.AnexceptionisChapter13onstochasticoptimalcontrol,whichalsorequiressomeconceptsinstochasticcalculus.Thoseconceptswillbeintroducedatthebeginningofthatchapter.Theprinciplemanagementscienceapplicationsdiscussedinthisbookareinthefollowingareas:financ

5、e,economics,productionandinventory,marketing,maintenanceandreplacement,andtheconsumptionofnatu•ralresources.Ineachmajorareawehaveformulatedoneormoresimplemodelsfollowedbyamorecomplicatedmodel.Thereadermaywishat21.WhatisOptimalControlTheory?firstreadingtocoveronlythesimplermodelsineachareatog

6、etanover•allideaofwhatispossibletodowithoptimalcontroltheory.Laterthereadermaywishtogointomoredepthintooneormoreoftheappliedareas.Worked-outexamplesareprovidedinmostchapterstofacilitatetheexposition.Attheendofeachchapter,wehavelistedexercisesthatthereadershouldsolvefordeepermiderstandingofth

7、ematerialpresentedinthechapter.Hintsaresuppliedwithsomeoftheexercises.Furthermore,difficultexercisesareindicatedwithanasterisk(*).1.1BasicConceptsandDefinitionsWeshallusethewordsystemasaprimitiveterminthisbook.Theonlypropertythatwerequireofasystemi