Under suitable controllability and smoothness assumptions, the minimum time function T(x) of a semilinear control system is proved to be locally Lipschitz continuous and semiconcave on the controllable set. These properties are then applied to derive optimality conditions relating optimal trajectories to the superdifferential of T.
Albano P., Cannarsa P., Sinestrari C. (2000). Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 38(3), 916-946 [10.1137/S0363012998335176].
Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type
Albano P.;
2000
Abstract
Under suitable controllability and smoothness assumptions, the minimum time function T(x) of a semilinear control system is proved to be locally Lipschitz continuous and semiconcave on the controllable set. These properties are then applied to derive optimality conditions relating optimal trajectories to the superdifferential of T.File in questo prodotto:
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