TY - JOUR

T1 - Trajectories of differential inclusions with state constraints

AU - Bressan, Alberto

AU - Facchi, Giancarlo

N1 - Funding Information:
The first author was partially supported by NSF through grant DMS-0807420, “New problems in nonlinear control”.

PY - 2011/2/15

Y1 - 2011/2/15

N2 - The paper deals with solutions of a differential inclusion ẋ∈ F(x) constrained to a compact convex set Ω. Here F is a compact, possibly non-convex valued, Lipschitz continuous multifunction, whose convex closure coF satisfies a strict inward pointing condition at every boundary point x∈∂Ω. Given a reference trajectory x*(·) taking values in an ε-neighborhood of Ω, we prove the existence of a second trajectory x:[0,T]→Ω which satisfies ||x-x*||W1,1{less-than above slanted equal above greater-than above slanted equal}Cε(1+|lnε|). As shown by an earlier counterexample, this bound is sharp.

AB - The paper deals with solutions of a differential inclusion ẋ∈ F(x) constrained to a compact convex set Ω. Here F is a compact, possibly non-convex valued, Lipschitz continuous multifunction, whose convex closure coF satisfies a strict inward pointing condition at every boundary point x∈∂Ω. Given a reference trajectory x*(·) taking values in an ε-neighborhood of Ω, we prove the existence of a second trajectory x:[0,T]→Ω which satisfies ||x-x*||W1,1{less-than above slanted equal above greater-than above slanted equal}Cε(1+|lnε|). As shown by an earlier counterexample, this bound is sharp.

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U2 - 10.1016/j.jde.2010.12.021

DO - 10.1016/j.jde.2010.12.021

M3 - Article

AN - SCOPUS:78650989140

SN - 0022-0396

VL - 250

SP - 2267

EP - 2281

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -