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

Published online by Cambridge University Press:  20 March 2008

Martino Bardi  and
Annalisa Cesaroni
Martino Bardi
Affiliation:
Dipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35131 Padova, Italy; bardi@math.unipd.it; acesar@math.unipd.it
Annalisa Cesaroni
Affiliation:
Dipartimento di Matematica P. e A., Università di Padova, via Trieste 63, 35131 Padova, Italy; bardi@math.unipd.it; acesar@math.unipd.it
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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.


Keywords

Controlled diffusionrobust controldifferential gameinvarianceviabilitystabilizationviscosity solutionoptimality principle
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 2 , April 2008 , pp. 343 - 355
Copyright
© EDP Sciences, SMAI, 2008

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