Calculus of Variations and Geometric Measure Theory

A class of control problems with measures data.

Ariela Briani (LMPT Université de Tours France)

created by depascal on 07 Jan 2010

13 jan 2010


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.