Pontryagin maximum principle and applications

ABSTRACTMaster ThesisPONTRYAGIN MAXIMUM PRINCIPLEandAPPLICATIONSMusa DERELİAnadolu UniversityGraduate School of SciencesMathematics ProgramSupervisor: Assist. Prof. Dr. Emrah AKYAR2006, 51 pagesThis thesis is a selection of some important results and numerous applicat-ions of the Pontryagin Maximum Principle which is one of the most importantresults of control theory and has applications to a variety of areas, from variousliteratures.First, the preliminaries which are required for later discussion are given andPontryagin Maximum Principle is stated and some optimal control problemsexamined through the Principle. The principle is, then, extended to generaltarget sets and non-autonomous systems are considered as well. Moreover, thesystems where the cost functions depend on time, state and control are alsoinvestigated and applications of all cases are given via several examples.Finally, a proof of Pontryagin Maximum Principle is given and the proofmethod is demonstrated on an example.Keywords: Control System, Pontryagin Maximum Principle, OptimalControl, General Targets, Cost Functionii