Geodesic
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 343-355

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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},
     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2007053/}
}
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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, Tome 14 (2008) no. 2, pp. 343-355. doi: 10.1051/cocv:2007053

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