Modeling, simulation, estimation and boundedness analysis of discrete event systems

In this paper, a particular state model allowing describing the system evolution in time is proposed. This state model contains two inequalities describing the evolution in time of the system state and input. The system simulation is based on the resolution of this state model. After that, a state estimator is proposed in order to estimate the whole system state and inputs. The state model and the observer are both proposed following count and dater approaches successively. In this work, the considered state is the number of transition firing if a count approach is followed and the dates of firing if the dater approach is considered. It is proved, using an illustrative example, that the proposed observer estimates well the system state by comparing the simulated and the estimated states. A boundedness analysis of the system trajectory is proposed in the case of FCF Petri nets. This analysis is based on an algorithm which gives the bounded transitions knowing the system input. Some particular tables are elaborated to describe the proposed algorithm. Theses tables give the bounded transitions after each iteration of the algorithm.