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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00395589/en/
Journal nameSIAM Journal on Control and Optimization
MetadataShow full item record
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 / KeywordsState constraints; Reachability set (Attainable set); Minimal time problem; Level set method; Hamilton-Jacobi-Bellman equations; Two-player game.
Showing items related by title and author.
L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1 Bokanowski, Olivier; Forcadel, Nicolas; Zidani, Hasnaa (2010) Article accepté pour publication ou publié