Traffic Models of Dynamic Periodic Event-Triggered Control Systems

Dynamic periodic event-triggered control (DPETC) is a type of event-triggered control (ETC) that inherits the excellent properties of ETC to avoid unnecessary communication and further extends the interevent intervals by introducing a dynamic variable. Despite their beneficiary effects, matters, such as communication scheduling, have been proposed due to the aperiodic execution manner. In this work, we focus on constructing an abstracted system, named traffic model. This model can capture the sampling behaviors generated by a DPETC system and is equivalent to a timed automaton. During the construction, we first confine the infinite state space to a finite number of regions. Then, the interevent interval related to each region is calculated by the linear matrix inequality technique. Finally, the reachability analysis is used to locate state transitions between different regions. A numerical example demonstrates the validity of the proposed construction approach.