Timed-arc Petri Nets modeling and forbidden state control approach

In this thesis, a new mathematical and graphical modeling method where time delays are assigned to arcs is presented for Timed Petri Nets. In Timed Petri Nets, states change by the flow of tokens with the time. This time-dependent movement causes an inability to track mathematical and graphical evaluation of the net during firing processes. In the proposed model, a triangular representation, called time element, that allows monitoring of tokens in transitions is introduced. Additionally, the state of the system at any time contains the marking vector representing the status of tokens in places and the remaining time vector representing the remaining time of tokens in transitions at that time. Expressing the state in terms of the marking and remaining time vectors makes it possible to obtain the reachability set and generate a timed-reachability tree. The controller design is also considered for the proposed mathematical model. Corresponding algorithms are developed for the construction of the reachability set and the controller design, and simulated with MATLAB. Results are presented through real-time and real-world case studies, such as manufacturing, railway, and automotive systems. In order to evaluate the performance of the proposed approach, it is compared with Stretched Petri Nets that is another modeling method for Timed Petri Nets.