1,721,188 research outputs found
La spiritualità di Giovanni Battista Montini
No full textColombo Giovanni. La spiritualità di Giovanni Battista Montini. In: Paul VI et la modernité dans l'Église. Actes du colloque de Rome (2-4 juin 1983) Rome : École Française de Rome, 1984. pp. 149-165. (Publications de l'École française de Rome, 72
The minimum time function for the controlled Moreau's sweeping process
Full text linkLet C(t), t ≥ 0 be a Lipschitz set-valued map with closed and (mildly non-)convex
values and f (t, x, u) be a map, Lipschitz continuous w.r.t. x. We consider the problem of reaching a
target S within the graph of C subject to the differential inclusion x ∈ −N_{C(t)} (x) + G(t, x) starting
̇from x_0 ∈ C(t_0 ) in the minimum time T (t_0 , x_0 ). The dynamics is called a perturbed sweeping (or
Moreau) process. We give sufficient conditions for T to be finite and continuous and characterize T
through Hamilton–Jacobi inequalities. Crucial tools for our approach are characterizations of weak
and strong flow invariance of a set S subject to the inclusion. Due to the presence of the normal cone
N_{C(t)} (x), the right-hand side of the inclusion contains implicitly the state constraint x(t) ∈ C(t) and
is not Lipschitz continuous with respect to x
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