Issue |
ESAIM: COCV
Volume 14, Number 2, April-June 2008
|
|
---|---|---|
Page(s) | 343 - 355 | |
DOI | https://doi.org/10.1051/cocv:2007053 | |
Published online | 20 March 2008 |
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
Dipartimento di Matematica P. e A., Università
di Padova, via Trieste 63, 35131 Padova, Italy;
bardi@math.unipd.it; acesar@math.unipd.it
Received:
11
January
2006
Revised:
26
October
2006
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.
Mathematics Subject Classification: 93D09 / 93E15 / 49L25 / 49N70
Key words: Controlled diffusion / robust control / differential game / invariance / viability / stabilization / viscosity solution / optimality principle
© EDP Sciences, SMAI, 2008
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