Sampling Performance of Periodic Event-Triggered Control Systems: A Data-Driven Approach

In this article, we employ the scenario optimization theory to compute a traffic abstraction, with probability guarantees of correctness, of a periodic event-triggered control (PETC) system with unknown dynamics from a finite number of samples. To this end, we extend the scenario optimization approach to multiclass support vector machines in order to compute a map between the concrete state space and the intersample times of the PETC. This map allows the construction of a traffic abstraction, through an $\ell$-complete relation, that provides upper and lower bounds on the sampling performance of the concrete system. We further propose an alternative path to build such abstraction; first, we identify the model and then apply a model-based procedure. Numerical benchmarks show the practical applicability of our methods for noiseless and noisy samples.