Optimization of hybrid Petri nets with shared variables

A generalized modeling framework for hybrid systems, including both discrete event and continuous-time dynamics, is presented in this paper. It is based on a new type of hybrid Petri nets, involving both modular structures, discrete shared variables and flexible transition predicates. The continuous-time dynamics is given by local differential equations, in a style similar to hybrid automata. This can be compared with existing hybrid Petri nets, where also the continuous-time dynamics is represented graphically, but then in reality limiting the continuous-time behavior to simple flow processes. The hybrid Petri net proposed in this paper works well for any type of continuous-time dynamics, including even differential inclusions, and the result is a compact, flexible and readable mix of graphical and equation based representations. The proposed modeling framework is also applied to a physical robot cell, where the energy consumption of the robot motions is minimized based on a hybrid Petri net model, easily transformed to a mixed integer nonlinear programming problem. The resulting optimization procedure is shown to reduce the energy consumption of the real robot cell by approximately 50%.