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

Cesaroni, Annalisa; Bardi, Martino

ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 343-355.

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.

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