École Nationale Supérieure de
Techniques Avancées

Abstract

This internship focuses on optimal control problem and more precisely on HAMILTON-JACOBI-BELLMAN theory. After some recalls on principal concepts such that viscosity solutions, dynamical programming principle, and optimal trajectory caracterisation, we focus on HJB equations on multidomains. With a precious link with an optimal control problem, it is possible to prove under precise assumptions about the dynamics the existence and the uniqness of the viscosity solution. Moreover we can then caracterize optimal trajectories. Finally, we explore briefly some numerical aspects but unfortunatly only on a practical way (without any proof of convergence), in order to get so hints about the difficulties relative to this kind of problems.