The evoluted set at time T is the union of all images of an initial set A via the flow at times t ∈ (0, T). Its regularity is for interest for control, being the attainable set in several relevant examples.We first show that it is not sufficient for A to have negligible boundary (i.e. zero Lebesgue measure) to ensure that the evoluted set has negligible boundary too. Instead, we prove that such property holds when A is a C1,1 domain.

When does the evoluted set have negligible boundary?

Boarotto F.;Rossi F.
2021

Abstract

The evoluted set at time T is the union of all images of an initial set A via the flow at times t ∈ (0, T). Its regularity is for interest for control, being the attainable set in several relevant examples.We first show that it is not sufficient for A to have negligible boundary (i.e. zero Lebesgue measure) to ensure that the evoluted set has negligible boundary too. Instead, we prove that such property holds when A is a C1,1 domain.
Proceedings of the IEEE Conference on Decision and Control
978-1-6654-3659-5
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11577/3444952
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