A hybrid Petri net formalism and resource allocation in distributed control systems

We propose a generalized concept of hybrid Petri nets as a modeling and design tool for the distributed dynamical systems involving asynchronous event-based communication. The proposed Petri net machine represents an extension of the standard discrete-event Petri nets, but differs conceptually from the conventional hybrid Petri nets in that dynamical processes are stored in the continuous places, similarly as in hybrid automata. In particular, the firing semantics of the corresponding continuous arcs is defined to capture the information exchange between the network nodes. While being primarily a graphical modeling tool, the proposed formalism of hybrid Petri nets infers a hybrid dynamical setting of event-triggered control problems, an approach that has been missing in the literature. The usability of our approach is illustrated in the context of the distributed event-triggered LQR and consensus problems, in conjunction with a systematic methodology for designing optimal adaptive scheduling schemes, governing the communication resources.