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: controlled diffusion, robust control, differential game, invariance, viability, stabilization, viscosity solution, optimality principle

@article{COCV_2008__14_2_343_0, author = {Cesaroni, Annalisa and Bardi, Martino}, title = {Almost sure properties of controlled diffusions and worst case properties of deterministic systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {343--355}, publisher = {EDP-Sciences}, volume = {14}, number = {2}, year = {2008}, doi = {10.1051/cocv:2007053}, mrnumber = {2394514}, zbl = {1133.93036}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2007053/} }

TY - JOUR AU - Cesaroni, Annalisa AU - Bardi, Martino TI - Almost sure properties of controlled diffusions and worst case properties of deterministic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 343 EP - 355 VL - 14 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2007053/ DO - 10.1051/cocv:2007053 LA - en ID - COCV_2008__14_2_343_0 ER -

%0 Journal Article %A Cesaroni, Annalisa %A Bardi, Martino %T Almost sure properties of controlled diffusions and worst case properties of deterministic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 343-355 %V 14 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2007053/ %R 10.1051/cocv:2007053 %G en %F COCV_2008__14_2_343_0

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://archive.numdam.org/articles/10.1051/cocv:2007053/

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