Data-driven Abstractions with Probabilistic Guarantees for Linear PETC Systems

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.