[CvGmt News] Seminari Calcolo delle Variazioni

depascal at dm.unipi.it depascal at dm.unipi.it
Thu Jan 7 12:50:21 CET 2010

A class of control problems with measures data.
   The first CVGMT seminar of the 2010 will be : 
   Wednesday Jan. 13 
   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 L^1-bilateral viscosity solution. For the latest we prove
   consistency, stability, and that the value function is indeed the
   unique L^1-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.

You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20100113/

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