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controlled diffusion

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Almost sure properties of controlled diffusionsand worst case properties of deterministic systems
Martino Bardi, Annalisa Cesaroni
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 14 / Issue 2 / April 2008

Published online by Cambridge University Press:

20 March 2008, pp. 343-355

Print publication:

April 2008
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We compare a general controlled diffusion process with a deterministic systemwhere a second controller drives the disturbance against the firstcontroller. We show that the two models are equivalent withrespect to two properties: the viability (or controlledinvariance, or weak invariance) of closed smooth sets, and theexistence of a smooth control Lyapunov function ensuring thestabilizability of the system at an equilibrium.