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

Martino Bardi; Annalisa Cesaroni

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 2, page 343-355
- ISSN: 1292-8119

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topBardi, Martino, and Cesaroni, Annalisa. "Almost sure properties of controlled diffusions and worst case properties of deterministic systems." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 343-355. <http://eudml.org/doc/250309>.

@article{Bardi2008,

abstract = {
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.
},

author = {Bardi, Martino, Cesaroni, Annalisa},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Controlled diffusion; robust control;
differential game; invariance; viability; stabilization; viscosity
solution; optimality principle; controlled diffusion; differential game; viscosity solution},

language = {eng},

month = {3},

number = {2},

pages = {343-355},

publisher = {EDP Sciences},

title = {Almost sure properties of controlled diffusions and worst case properties of deterministic systems},

url = {http://eudml.org/doc/250309},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Bardi, Martino

AU - Cesaroni, Annalisa

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/3//

PB - EDP Sciences

VL - 14

IS - 2

SP - 343

EP - 355

AB -
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.

LA - eng

KW - Controlled diffusion; robust control;
differential game; invariance; viability; stabilization; viscosity
solution; optimality principle; controlled diffusion; differential game; viscosity solution

UR - http://eudml.org/doc/250309

ER -

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