Calculus of Variations and Geometric Measure Theory

M. Bardi - A. Cesaroni

Almost sure properties of controlled diffusions and worst case properties of deterministic systems

created by bardi on 06 Sep 2007
modified on 01 Aug 2008


Published Paper

Inserted: 6 sep 2007
Last Updated: 1 aug 2008

Journal: ESAIM Control Optim. Calc. Var.
Volume: 14
Number: 2
Pages: 343-355
Year: 2008


We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.

Keywords: differential games, controlled diffusion processes, viability, stabilization