Modeling and Optimization of Hybrid Systems*

In this paper a predicate transition model for discrete event systems is generalized to include continuous dynamics, and the result is a modular hybrid predicate transition model. Based on this model a hybrid Petri net, including explicit differential equations and shared variables, is also proposed. It is then shown how this hybrid Petri net model can be optimized based on a simple and robust nonlinear programming formulation. The procedure only assumes that desired sampled paths for a number of interacting moving devices are given, while originally equidistant time instances are adjusted to minimize a given criterion. This optimization of hybrid systems is also applied to a real robot station with interacting devices, which results in about 30% reduction in energy consumption.