What ODE-Approximation Schemes of Time-Delay Systems Reveal about Lyapunov-Krasovskii Functionals

Scholl, Tessina H.; Hagenmeyer, Veit; Gröll, Lutz

doi:10.48550/arxiv.2202.13122

Search citation statements

Order By: Relevance

Paper Sections

Select...

Corollary 4 Given a Cbfal  And A Locally Lipschitz Continuo...1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Corollary 5. If  is a CBFal for (53) on  defined by (20), then any locally Lipschitz continuous controller 50) ∀x t ∈  renders set S forward invariant w.r.t. ( 54).…”

Section: Corollary 4 Given a Cbfal  And A Locally Lipschitz Continuo...mentioning

confidence: 99%

Control barrier functionals: Safety‐critical control for time delay systems

Molnár

Ames

Orosz

2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

show abstract

“…Corollary 5. If  is a CBFal for (53) on  defined by (20), then any locally Lipschitz continuous controller 50) ∀x t ∈  renders set S forward invariant w.r.t. ( 54).…”

Section: Corollary 4 Given a Cbfal  And A Locally Lipschitz Continuo...mentioning

confidence: 99%