A Primer on the Calculus of Variations and Optimal Control Theory

Thecalculusofvariationsisusedtofindfunctionsthatoptimizequantitiesexpressedintermsofintegrals.Optimalcontroltheoryseekstofindfunctionsthatminimizecostintegralsforsystemsdescribedbydifferentialequations.Thisbookisanintroductiontoboththeclassicaltheoryofthecalculusofvariationsandthemoremoderndevelopmentsofoptimalcontroltheoryfromtheperspectiveofanappliedmathematician.Itfocusesonunderstandingconceptsandhowtoapplythem.Therangeofpotentialapplicationsisbroad:thecalculusofvariationsandoptimalcontroltheoryhavebeenwidelyusedinnumerouswaysinbiology,criminology,economics,engineering,finance,managementscience,andphysics.Applicationsdescribedinthisbookincludecancerchemotherapy,navigationalcontrol,andrenewableresourceharvesting.Theprerequisitesforthebookaremodest:thestandardcalculussequence,afirstcourseonordinarydifferentialequations,andsomefacilitywiththeuseofmathematicalsoftware.Itissuitableforanundergraduateorbeginninggraduatecourse,orforselfstudy.Itprovidesexcellentpreparationformoreadvancedbooksandcoursesonthecalculusofvariationsandoptimalcontroltheory.