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

Abstract

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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.


How to cite

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Bardi, 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 -

References

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