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SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Martedì 15 Ottobre 2013 alle ore 15:00 in aula 2BC30, Athena Picarelli (INRIA, Parigi) terrà un seminario dal titolo "Dynamic programming for stochastic optimal control problems with a maximum cost"
This work is concerned with stochastic optimal control for a cost depending on a running maximum. The results presented can be applied to the case of lookback options in finance, moreover it will be shown how this kind of problems arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton-Jacobi-Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme.
A seguire Hasnaa Zidani (ENSTA ParisTech, Parigi) terrà un seminario dal titolo "Rechability Analysis and motion planning"
Because of their importance in many applications, questions of path planning and reachability analysis for nonlinear dynamical systems have been studied extensively in the control theory. Here we focus on the cases when the controlled systems are constrained to evolve in a certain known set (e.g avoidance of obstacles). We study general framework based on an optimal control approach and on solving Hamilton-Jacobi (HJ) equations. This approach provides a very efficient tool for treating many cases encountered in real applications and can be extended to general situations including moving targets and/or obstacles problems, dynamical systems under uncertainties, or differential games. The relevance of the method will be shown on some numerical examples (motion planning with obstacle avoidance).
M. Bardi, C. Marchi, F. Ancona