Document ESAIM: COCV, Vol. 14, N°2, pp. 343-355
DOI: 10.1051/cocv:2007053
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
Martino Bardi and Annalisa CesaroniDipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35131 Padova, Italy; bardi@math.unipd.it; acesar@math.unipd.it
(Received January 11, 2006. Revised October 26, 2006. Published online October 13, 2007.)
Abstract
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.
Mathematics Subject Classification. 93D09, 93E15, 49L25, 49N70
Key words: Controlled diffusion, robust control, differential game, invariance, viability, stabilization, viscosity solution, optimality principle
© EDP Sciences, SMAI 2008