Data-Driven Krasovskii Approach to Safety Controllers for Time-Delayed Uncertain Polynomial Systems

Data-Driven Krasovskii Approach to Safety Controllers for Time-Delayed Uncertain Polynomial Systems

The authors Omid Akbarzadeh, MohammadHossein Ashoori, Amy Nejati and Abolfazl Lavaei present a framework for designing safety controllers for discrete-time systems with uncertain polynomial dynamics, time-invariant delays and unknown-but-bounded disturbances. Their approach uses observed input-state data rather than requiring an explicit system model. It builds robust Krasovskii control barrier certificates by incorporating delayed components, then formulates the design as a data-driven sum-of-squares feasibility program. The authors say robust safety is guaranteed only while closed-loop trajectories remain within the state set. They report demonstrating the method in three case studies, including two physical systems. The proposal addresses a specific difficulty in safety design: accounting for delays and disturbances when the system model is unavailable. The abstract does not report the case-study outcomes or explain how performance varies across them.

Publication: 74855862-3798-4f2b-8a66-e9095b213aa2

attribution — pass: The four named authors match the arXiv listing, and the framework, safety guarantee and case-study claims are attributed to them rather than stated as established fact.

Authors:Omid Akbarzadeh, MohammadHossein Ashoori, Amy Nejati, Abolfazl Lavaei

summary — uncertain: The reading tracks the abstract, but a non-specialist could not follow it. Central terms are used without plain explanation: control barrier certificates, sum-of-squares feasibility program, closed-loop trajectories, state set, input-affine and polynomial dynamics. It never says what a safety controller does: keep a controlled system out of unsafe states. The term library should cover these terms. It also does not explain plainly why delays and missing models matter. Smallest repair: add one plain sentence each on what a barrier certificate and safety controller do, and why learning them from data is useful when no model exists.

first, the system's mathematical model is unavailable; and second, the safety conditions should explicitly incorporate the effects of time delays

date — pass: originalPublished 2026-01-28 matches the v1 submission date. The 1 Nov 2026 date is a later revision (v2), and the November feed date is not the first publication.

[Submitted on 28 Jan 2026 (v1), last revised 1 Nov 2026 (this version, v2)]

support — uncertain: The source states a sufficient condition: safety holds as long as trajectories stay within the state set. The summary says the guarantee holds only while that is true, and claim 3 says only as long as. Adding only turns a sufficient condition into a necessary one, which the abstract does not state. The smallest repair is to drop only and use the source's as long as wording. The other claims are supported verbatim, and the question about case-study outcomes follows fairly from the abstract.

robust safety is guaranteed in the presence of unknown disturbances and time delays as long as the closed-loop trajectories remain within the state set.

media — pass: The selected media is the verified arXiv abstract page for this paper. It is the direct original source, and no better source media was found.