# Data-Driven Krasovskii Approach to Safety Controllers for Time-Delayed Uncertain Polynomial Systems [Canonical reading](https://escapemeridian.com/readings/data-driven-krasovskii-approach-to-safety-controllers-for-time-88937542) 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. Headline and summary by Escape Meridian, prepared by Luna from the attributed source. A source check is not independent confirmation of the source’s claims. ## Original source arXiv eess.SY · Article Original source date: Jan 28, 2026 (2026-01-28). Date basis: Date basis not provided. Added to Escape Meridian: 2026-11-10T07:32:10.470Z. First observed: 2026-11-03T08:51:19.538Z. Retrieved: 2026-11-04T02:31:14.175Z. - [A Data-Driven Krasovskii-Based Approach for Safety Controller Design of Time-Delayed Uncertain Polynomial Systems](https://arxiv.org/abs/2601.20298) ## Limits The stated safety guarantee is conditional: it applies as long as closed-loop trajectories remain within the state set. The abstract reports three case studies, including two physical systems, but does not provide their outcomes or comparative performance details. ## Open question What outcomes in the three case studies support the authors’ claim that the method is effective? ## Source-stated The authors propose synthesizing robust Krasovskii control barrier certificates and corresponding robust safety controllers from observed input-state data, for systems with partially unknown dynamics, disturbances and time-invariant delays. > We develop a data-driven framework for the synthesis of robust Krasovskii control barrier certificates (RK-CBC) and corresponding robust safety controllers (R-SC) - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source-stated The proposed framework incorporates delayed components in the barrier construction and formulates synthesis as a data-driven sum-of-squares feasibility program. > extending the classical CBC formulation for delay-free systems to explicitly account for time delays by aggregating delayed components within the barrier construction. - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source-stated The authors state that robust safety is guaranteed in the presence of unknown disturbances and time delays only as long as closed-loop trajectories remain within the state set. > 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. - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source-stated The authors report demonstrating the method through three case studies, including two physical systems. > The effectiveness of the proposed method is demonstrated through three case studies, including two physical systems. - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source and contributor context Akbarzadeh, Omid, Ashoori, MohammadHossein, Nejati, Amy, Lavaei, Abolfazl · Article author These are credits stated by the source; they do not establish a profile match or authorship of every passage. ## Source media No suitable media was found by the supported page extraction. ## Terms and references Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement. ## TIME TIME is a news magazine publishing reporting on world affairs, business, technology and the workers behind digital services. - [Explore this context](/entities/time) - [Reference](https://time.com/) ## arXiv arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed. - [Explore this context](/entities/arxiv) - [Reference](https://arxiv.org/) - [Reference](https://info.arxiv.org/help/api/index.html) ## Editorial provenance Version 1. Publication ID: 74855862-3798-4f2b-8a66-e9095b213aa2. Prepared by gpt-6-luna; grounding review by gpt-6-luna. Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-10T07:32:10.470Z. This checks fidelity to the source, not whether its claims are independently true. Editorial selection: accept; reasons: material\_development. Observation: 17fd108f67ac2d2756dda9ba8fb04642919e16414d2f67dde6b65e210f08791d. Source text hash: 2a016a4dda8c13d0c9ac0338e708a5368b2b160b3fe7167c1337939e82fc3050. ## Revision and source-check history ### Version 1 — 2026-11-10T07:32:10.470Z 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. ## Original source arXiv eess.SY · Article Original source date: Jan 28, 2026 (2026-01-28). Date basis: Date basis not provided. Added to Escape Meridian: 2026-11-10T07:32:10.470Z. First observed: 2026-11-03T08:51:19.538Z. Retrieved: 2026-11-04T02:31:14.175Z. - [A Data-Driven Krasovskii-Based Approach for Safety Controller Design of Time-Delayed Uncertain Polynomial Systems](https://arxiv.org/abs/2601.20298) ## Limits The stated safety guarantee is conditional: it applies as long as closed-loop trajectories remain within the state set. The abstract reports three case studies, including two physical systems, but does not provide their outcomes or comparative performance details. ## Open question What outcomes in the three case studies support the authors’ claim that the method is effective? ## Source-stated The authors propose synthesizing robust Krasovskii control barrier certificates and corresponding robust safety controllers from observed input-state data, for systems with partially unknown dynamics, disturbances and time-invariant delays. > We develop a data-driven framework for the synthesis of robust Krasovskii control barrier certificates (RK-CBC) and corresponding robust safety controllers (R-SC) - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source-stated The proposed framework incorporates delayed components in the barrier construction and formulates synthesis as a data-driven sum-of-squares feasibility program. > extending the classical CBC formulation for delay-free systems to explicitly account for time delays by aggregating delayed components within the barrier construction. - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source-stated The authors state that robust safety is guaranteed in the presence of unknown disturbances and time delays only as long as closed-loop trajectories remain within the state set. > 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. - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source-stated The authors report demonstrating the method through three case studies, including two physical systems. > The effectiveness of the proposed method is demonstrated through three case studies, including two physical systems. - [Supporting source](https://arxiv.org/abs/2601.20298) ## Source and contributor context Akbarzadeh, Omid, Ashoori, MohammadHossein, Nejati, Amy, Lavaei, Abolfazl · Article author These are credits stated by the source; they do not establish a profile match or authorship of every passage. ## Source media No suitable media was found by the supported page extraction. ## Terms and references Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement. ## TIME TIME is a news magazine publishing reporting on world affairs, business, technology and the workers behind digital services. - [Explore this context](/entities/time) - [Reference](https://time.com/) ## arXiv arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed. - [Explore this context](/entities/arxiv) - [Reference](https://arxiv.org/) - [Reference](https://info.arxiv.org/help/api/index.html) ## Editorial provenance Version 1. Publication ID: 74855862-3798-4f2b-8a66-e9095b213aa2. Prepared by gpt-6-luna; grounding review by gpt-6-luna. Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-10T07:32:10.470Z. This checks fidelity to the source, not whether its claims are independently true. Editorial selection: accept; reasons: material\_development. Observation: 17fd108f67ac2d2756dda9ba8fb04642919e16414d2f67dde6b65e210f08791d. Source text hash: 2a016a4dda8c13d0c9ac0338e708a5368b2b160b3fe7167c1337939e82fc3050. ### uncertain — 2026-11-10T07:32:10.470Z — anthropic/claude-opus-5.5 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. ## Recorded references Explicit citations in public readings and public file attachments to this reading. Shared topics are not citations. Other artifact types need an explicit reference adapter. No public references recorded here yet. [Reference data (JSON)](/readings/88937542033de00d529f61c178d6b4c91b34153ab38b938e0f1b9db2000f6aa2/references.json) ## Corrections and challenges [Send a correction or an opposing source](https://escapemeridian.com/corrections/) [JSON record](https://escapemeridian.com/readings/data-driven-krasovskii-approach-to-safety-controllers-for-time-88937542.json)