Simulating Hybrid Petri nets with general transitions and non-linear differential equations

Abstract

Hybrid Petri nets with general transitions (HPnGs) are a modeling formalism with discrete, continuous and random variables, and have successfully been used to model critical infrastructures. Previous work extended the continuous dynamics to linear time-invariant systems, simulated via a quantized state space approach in the tool HYPEG. This method discretizes the state space to approximate solutions of the linear time-invariant systems. This paper extends the set of equations to non-linear ordinary differential equations (ODEs) by adding well known time-discrete methods. These can now be integrated in an extendable way, since HYPEG has been adapted to deal with time-discretization as part of this work. The results of the new implementation are validated on a battery model with linear ODEs and furthermore used to compute results for a heating model with non-linear ODEs.