A Compositional Model for Multi-Rate Max-Plus Linear Systems

The timing of discrete-event systems with synchronization is naturally modeled with canonical multi-rate max-plus linear equations. The main objectives of these models are to analyze and control the systems. As a system becomes more complex, determining its canonical model becomes more complicated. Moreover, these systems may change over time which demands the model to be recalculated. Motivated by the compositional structure of many systems, we propose operations to determine the canonical model for composed multi-rate max-plus linear systems. The operations allow efficient (re-)calculation of the canonical models from constituent canonical models. These models can be utilized to analyze and/or control complex systems using existing methods.