Petri Nets as Run-Time Models for Self-Adaptive Cyber-Physical Systems Cost-Benefit Analysis of Structural Transformations

In our general research we study adaptive systems of autonomous agents – with a strong emphasis on agents in cyber-physical systems (CPS). To enable adaptivity, we have a special interest in agents that are embedded into an overall structure, called: organisation. Our Sonar formalism is a specification of the organisational structure; it is based on Petri nets. In this contribution we investigate the whole life-cycle of Sonar models, from (i) the analytical usage in the design phase, over (íi) their use as configuration data in the deployment phase, to (iii) their use as a digital twin used for cost-benefit reasoning at run-time during the Sonar-MAPE-Loop. We also present a rule set of transformations for Sonar models. These rules are applicable at different phases of the life cycle: They are used by the modeller at design time, e.g. to refine an early, abstract model into a more concrete one; they are also used by the run-time engine, i.e., the Sonar-MAPE-Loop, as adaption operations during a self-modification. Remarkably, these two phases – design and run-time – are intertwined in a cyclic way: Obviously, the Sonar-model (usually amended by an deployment profile, called cube-protocols) is used to instantiate the running multi-agent system; but, conversely, we use process mining techniques to (i) adjust the deployment profile in a re-configuration phase or (ii) to trigger a complete re-design phase of the Sonar-model.