Almost sure properties of controlled diffusions and worst case properties of deterministic systems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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.

DOI: 10.1051/cocv:2007053
Classification: 93D09,  93E15,  49L25,  49N70
Keywords: controlled diffusion, robust control, differential game, invariance, viability, stabilization, viscosity solution, optimality principle
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author = {Cesaroni, Annalisa and Bardi, Martino},
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Cesaroni, Annalisa; Bardi, Martino. Almost sure properties of controlled diffusions and worst case properties of deterministic systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 2, pp. 343-355. doi : 10.1051/cocv:2007053. http://www.numdam.org/articles/10.1051/cocv:2007053/

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