Data‐driven abstractions based on deep learning for periodic event‐triggered control systems

Abstract Abstract model of periodic event‐triggered control (PETC) system can help explore the sampling behaviors of the event‐triggered manner; thus, it is necessary to build scheduling schemes. In this work, a scenario‐based approach is adopted to construct an abstract model of an unknown PETC system based on finite number of samples. More specifically, this scenario method is applied to the learning process of a neural network in order to construct a probably approximate correct (PAC) mapping between the state evolution and the intersample times. For the construction of the abstract model, the state space is first partitioned into finite regions; the model can be obtained based on the partition and the learning result. The model gives the reachable regions starting from each region and provides the lower and upper bounds of the sampling interval of each region. Numerical benchmarks include a smart water distribution system that demonstrates the practical applicability of the presented method.