Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Giulia Fabrini (Universität Konstanz)

Diese Veranstaltung ist Teil der Veranstaltungsreihe „Frauen in der Mathematik“.

Abstract: The theory of control analyses the properties of controlled systems, i.e. dynamical systems on which we can act through a function called control. The aim is to bring the system from an initial state to a certain final state satisfying some criteria. There are two different types of control: open-loop controls, which depend on the time variable and feedback controls, which depend on the state variable. The second ones are more appealing since they are robust to external perturbations. However, the synthesis of feedback controls requires the solution of a nonlinear Hamilton-Jacobi-Bellman equation (HJB). Due to the complexity of finding an analytical solution to this equation, several approximations schemes have been proposed. The major bottleneck of these numerical schemes is that they suffer from the so called  "curse of dimensionality”, since the dimension of the discretised equation increases as the dimension of the state space does. An alternative way to find control in feedback form is a method known as Model Predictive Control (MPC).  In this talk we give an introduction to the HJB and MPC approaches and also propose a coupling of them.  Finally, we present some numerical tests to show the efficiency of the proposed algorithm.