Control óptimo de sistemas discretos e ecuacións diferenciais ordinarias

Abstract

Neste traballo estudaranse os problemas de control óptimo sen restricións, tanto no caso discreto coma no continuo. O primeiro que se buscará nestes problemas será, proporcionar métodos que permitan o cálculo do gradiente do funcional custo, ˜ J, no caso discreto. Estes particularizaranse no caso onde o problema sexa evolutivo, aproveitando esta estrutura para reducir o custo computacional. No caso continuo consideraranse problemas onde o estado veña dado por unha EDO. A forma na que se abordarán estes problemas consistirá en: discretizar o problema de maneira que entre no marco das seccións anteriores, ou calcular as derivadas direccionais de ˜ J, mediante métodos que se proporcionarán neste traballo, permitindo así o cálculo do gradiente ao aproximar o espazo de control por un de dimensión finita. Os métodos do caso discreto empregaranse para resolver problemas de estimación de parámetros, mentres que os do caso continuo resolverán un problema relacionado co movemento dun sistema carro-péndulo.

In this work we will study optimal control problems without restrictions, both in the discrete and continuous cases. The first thing that will be sought in these problems will be to provide methods that allow to calculate the gradient of the cost functional, ˜ J, in the discrete case. These will be particularized in the case where the problem is evolutionary, taking advantage of this structure to reduce the computational cost. In the continuous case, problems where the state is given by an EDO will be considered. The way in which these problems will be approached will consist of: discretizing the problem so that it falls within the framework of the previous sections, or calculating the directional derivatives of the cost functional, using methods that will be provided in this work, thus allowing the gradient to be calculated by approximating the control space by a finite-dimensional space. The methods of the discrete case will be used to solve parameter estimation problems, while those of the continuous case will solve a problem related to the motion of a cart-pole system.