Data-driven Abstractions with Probabilistic Guarantees for Linear PETC Systems
This work addresses the challenge of analyzing event-triggered control systems without full models, which is important for control engineers, but it is incremental as it builds on existing scenario and SVM methods.
The paper tackles the problem of estimating average inter-sample times for unknown linear PETC systems by using a scenario approach to compute probably approximately correct bounds from finite samples, and numerical benchmarks demonstrate its practical applicability compared to model-based state-of-the-art tools.
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.