Scalable Traffic Models for Scheduling of Linear Periodic Event-Triggered Controllers

This paper addresses the problem of modeling and scheduling the transmissions generated by multiple event-triggered control (ETC) loops sharing a network. We present a method to build a symbolic traffic model of periodic ETC (PETC), which by construction provides an exact simulation of such traffic. The model is made in such a way as to avoid the combinatorial explosion that is typical of symbolic models in many applications. It is augmented with early triggering actions that can be used by a scheduler to mitigate communication conflicts. The complete networked control system is then modeled as a network of timed game automata, for which existing tools can generate a strategy that avoids communication conflicts, while keeping early triggers to a minimum. By construction, our proposed symbolic model is a quotient model of the PETC. It is relatively fast to build, and it generates few to no spurious transitions. We finally demonstrate modeling and scheduling for a numerical example.