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Reachability and minimal times for state constrained nonlinear problems without any controllability assumption

Zidani, Hasnaa; Forcadel, Nicolas; Bokanowski, Olivier (2010), Reachability and minimal times for state constrained nonlinear problems without any controllability assumption, SIAM Journal on Control and Optimization, 48, 7, p. 4292-4316. http://dx.doi.org/10.1137/090762075

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00395589/en/
Date
2010
Journal name
SIAM Journal on Control and Optimization
Volume
48
Number
7
Publisher
SIAM
Pages
4292-4316
Publication identifier
Metadata
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Author(s)
Zidani, Hasnaa
Forcadel, Nicolas cc
Bokanowski, Olivier cc
Abstract (EN)
We consider a target problem for a nonlinear system under state constraints. We give a new continuous level-set approach for characterizing the optimal times and the backward-reachability sets. This approach leads to a characterization via a Hamilton-Jacobi equation, without assuming any controllability assumption. We also treat the case of time-dependent state constraints, as well as a target problem for a two-player game with state constraints. Our method gives a good framework for numerical approximations, and some numerical illustrations are included in the paper.
Subjects / Keywords
State constraints; Reachability set (Attainable set); Minimal time problem; Level set method; Hamilton-Jacobi-Bellman equations; Two-player game.