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- W3102331880 abstract "Let $C(t)$, $tgeq0$ 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 [ (star)qquad dot{x} in -N_{C(t)}(x) + G(t,x) ] starting from $x_{0}in C(t_{0})$ in the minimum time $T(t_{0},x_{0})$. The dynamics $(star)$ 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 $(star)$. Due to the presence of the normal cone $N_{C(t)}(x)$, the right hand side of $(star)$ contains implicitly the state constraint $x(t)in C(t)$ and is not Lipschitz continuous with respect to $x$." @default.
- W3102331880 created "2020-11-23" @default.
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- W3102331880 date "2016-01-01" @default.
- W3102331880 modified "2023-09-25" @default.
- W3102331880 title "The Minimum Time Function for the Controlled Moreau's Sweeping Process" @default.
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- W3102331880 doi "https://doi.org/10.1137/15m1043364" @default.
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