# Data-driven Abstractions with Probabilistic Guarantees for Linear PETC Systems

arXiv: https://arxiv.org/abs/2203.05522 · HTML: https://mlsanity.com/paper/2203.05522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 10 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise](https://mlsanity.com/paper/2110.12662/) (2021)
- [Scenario-Based Verification of Uncertain MDPs](https://mlsanity.com/paper/1912.11223/) (2019)
- [Symbolic Abstractions From Data: A PAC Learning Approach](https://mlsanity.com/paper/2104.13901/) (2021)
- [A Formal Traffic Characterization of LTI Event-triggered Control Systems](https://mlsanity.com/paper/1503.05816/) (2015)
- [Scalable Traffic Models for Scheduling of Linear Periodic Event-Triggered Controllers](https://mlsanity.com/paper/2003.07642/) (2020)
- [Towards Traffic Bisimulation of Linear Periodic Event-Triggered Controllers](https://mlsanity.com/paper/2005.14504/) (2020)
- [Computing the sampling performance of event-triggered control](https://mlsanity.com/paper/2103.00919/) (2021)
- [Chaos and order in event-triggered control](https://mlsanity.com/paper/2201.04462/) (2022)
- [ETCetera: beyond Event-Triggered Control](https://mlsanity.com/paper/2203.01623/) (2022)

## Built on by (most cited first, 1 of 1)

- [Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty](https://mlsanity.com/paper/2210.05989/) (2022)

## Abstract (arXiv)

We employ the scenario approach to compute probably approximately correct (PAC) bounds on the average inter-sample time (AIST) generated by an unknown PETC system, based on a finite number of samples. We extend the scenario approach to multiclass SVM algorithms in order to construct a PAC map between the concrete, unknown state-space and the inter-sample times. We then build a traffic model applying an ℓ-complete relation and find, in the underlying graph, the cycles of minimum and maximum average weight: these provide lower and upper bounds on the AIST. Numerical benchmarks show the practical applicability of our method, which is compared against model-based state-of-the-art tools.