Modified particle petri nets for hybrid dynamical systems monitoring under environmental uncertainties

A real-time system in its environment constitutes a complex dynamic system (in general hybrid), which requires the development of new methods of modeling and monitoring. This paper presents the Modified Particle Petri nets (MPPN) approach, which combines Petri nets and particle filtering in order to model and monitor Hybrid Dynamical Systems (HDS) and their interaction with the environment. The approach considers the uncertainty of the process on both discrete and continuous variables as well as the environmental uncertainties. It presents relevant concepts of Petri nets within a probabilistic framework and how uncertainty is introduced (i) in the hybrid marking of the Petri net in order to represent an uncertain knowledge about all next possible hybrid states (ii) as well as in the process noise, which is incorporated into the filter. A marking updating of the Petri nets according to noisy measurements made by the system and a decision making algorithm are then used in order to estimate the hybrid system state, to detect inconsistencies and to attribute these to different kinds of faults. An example of mobile robot application modeled using MPPN is presented to show the usability of the approach.