Corcuera Valverde, José ManuelMuñoz Ruz, Rubén2015-02-062015-02-062014-06-24https://hdl.handle.net/2445/62444Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2014, Director: José Manuel Corcuera ValverdeThe aim of this end of degree work is to analyze a few problems studied by the optimal control theory using the Pontryagin’s maximum principle. It is divided into three distinct parts: in the first one we introduce the calculus of variations theory, in the second one we present the optimal control theory and the maximum principle and we show that this theory can be treated as an extension of calculus of variations; and, finally, in the last part we expose how the optimal control theory can be extended considering some randomness, that is to say, for cases involving stochastic processes.51 p.application/pdfspacc-by-nc-nd (c) Rubén Muñoz Ruz, 2014http://creativecommons.org/licenses/by-nc-nd/3.0/esCàlcul de variacionsTreballs de fi de grauTeoria de controlProcessos estocàsticsEquacions diferencials ordinàriesSistemes dinàmics diferenciablesCalculus of variationsBachelor's thesesControl theoryStochastic processesOrdinary differential equationsDifferentiable dynamical systemsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess