13 jan 2010
Abstract.
The first CVGMT seminar of the 2010 will be : Wednesday Jan. 13
At 17 Aula Seminari, Dipartimento di matematica.
Ariela Briani (Univ. di Pisa & ENSTA )
Title: A class of control problems with measures data.
Abstract: Motivated by models of heavy space launcher we consider in 1 a final state constrained optimal control problem with measure data. More precisely, we model the problem of steering a heavy space launcher to the GTO orbit with minimal propellant consumption and with a fixed final mass. I will first show that it is related to a standard front propagation problem via the reachability function and therefore I will study the related Hamilton-Jacobi-Bellmann (HJB) equation. In 2 , to characterize the value function we first use the graph completion technique to reparametrize our problem and to give a "viscosity sense" to the HJB equation. Secondly, to deal simultaneously with a lower semi continuous final condition and t-measurable Hamiltonian we give a new definition of L1-bilateral viscosity solution. For the latest we prove consistency, stability, and that the value function is indeed the unique L1-bilateral viscosity solution of the HJB equation.
1 O. Bokanowski, A. Briani and H. Zidani, Minimum time control problems for non autonomous differential equations, Systems & Control Letters, vol. 58, pp. 742--746, 2009. 2 A. Briani, H. Zidani, Characterization of the value function of final state constrained conrtrol problems with BV trajectories, preprint.