Modeling and simulation of hybrid dynamical systems with generalized differential Petri nets

There has been considerable interest in the modeling and simulation of hybrid dynamic systems (HDS). As an effective modeling tool of discrete event dynamic systems, Petri nets have a dual nature of a graphical tool and a mathematical object. In this paper, an extension of Petri net named generalized differential Petri nets (GDPN) is proposed to model HDS that have a combination of discrete-event evolution and continuous state evolution. Differential place and differential transition defined by Demongodin et al. (1998) are used to model the numeral simulation of the continuous dynamic process, and the weights defined on the directed arcs that connects the differential transitions and places are extended from real numbers to real matrices. The marking of differential place are also enlarged from real numbers to real vectors. Then the evolution rules and modeling method of HDS with GDPN are introduced. Two examples are used to illustrate the modeling power of GDPN in HDS.