Vieiro Yanes, ArturoReal Casals, Anna2020-06-152020-06-152020-01-19https://hdl.handle.net/2445/165520Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Arturo Vieiro Yanes[en] The main objective of this study is the analysis of the behavior of continuous dynamic systems. The key to this study is the control, a variable that drives the system to achieve a fixed final state. Controllability, observability and stability are aspects that affect the choice of an adequate control. Attention has been focused on two types of control. The first one is the PID control, which is focused on feedback to produce a proportional, derivative and integral adjustment on the system, hence its name. This control has been implemented for the classical pendulum under the action of the gravitational force and without friction. The other one is the optimal control. The objective of this control for the dynamic system is to optimize a functional. The conditions have been studied to ensure that a control is an optimal control in different situations.60 p.application/pdfcatcc-by-nc-nd (c) Anna Real Casals, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Equacions diferencials ordinàriesTreballs de fi de grauTeoria de controlFuncions de LyapunovOrdinary differential equationsBachelor's thesesControl theoryLyapunov functionsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess