A Relaxation Result for State-Constrained Delay Differential Inclusions

Abstract : In this paper, we consider a delay differential inclusion ˙ x(t) ∈ F (t, xt), where xt denotes the history function of x(t) along an interval of time. We extend the celebrated Filippov's theorem to this case. Then, we further generalize this theorem to the case when the state variable x is constrained to the closure of an open subset K ⊂ R n. Under a new "inward pointing condition", we give a relaxation result stating that the set of trajectories lying in the interior of the state constraint is dense in the set of constrained trajectories of the convexified inclusion ˙ x(t) ∈ co F (t, xt).
Document type :
Journal articles
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02126119
Contributor : Helene Frankowska <>
Submitted on : Friday, May 10, 2019 - 8:57:03 PM
Last modification on : Sunday, May 19, 2019 - 1:13:18 AM

File

Version4.pdf
Files produced by the author(s)

Identifiers

Citation

Hélène Frankowska, Ihab Haidar. A Relaxation Result for State-Constrained Delay Differential Inclusions. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2018, 63 (11), pp.3751-3760. ⟨10.1109/TAC.2018.2794398⟩. ⟨hal-02126119⟩

Share

Metrics

Record views

25

Files downloads

36