Data-driven Abstractions with Probabilistic Guarantees for Linear PETC Systems

TL;DR

This paper introduces a data-driven method using the scenario approach to estimate probabilistic bounds on inter-sample times in unknown PETC systems, leveraging multiclass SVMs and traffic modeling for practical bounds.

Contribution

It extends the scenario approach to multiclass SVMs for constructing PAC maps and applies traffic modeling to derive bounds on inter-sample times in PETC systems.

Findings

Method provides probabilistic bounds on inter-sample times.

Numerical benchmarks demonstrate practical applicability.

Compared favorably against existing model-based tools.

Abstract

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 $\ell$-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.