Almost sure properties of controlled diffusions and worst case properties of deterministic systems
Dipartimento di Matematica P. e A., Università
di Padova, via Trieste 63, 35131 Padova, Italy;
Revised: 26 October 2006
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