In this paper a cyclic place-timed controlled marked graph (PTCMG), which is an extended class of a cyclic controlled marked graph (CMG), is presented as a model of discrete event systems (DESs). In a PTCMG, time constraints are attached to places instead of transitions. The time required for a marked place to be marked again is represented in terms of time constraints attached to places. The times required for an unmarked place to be marked under various controls, are calculated. The necessary and sufficient condition for a current marking to be in the admissible marking set with respect to the given forbidden condition is provided, as is the necessary and sufficient condition for a current marking to be out of the admissible marking set with respect to the forbidden condition in one transition. A maximally permissive state feedback control is synthesized in a PTCMG to guarantee a larger admissible marking set than a CMG for most forbidden state problems. Practical applications are illustrated for a railroad crossing problem and an automated guided vehicle (AGV) coordination problem in a flexible manufacturing facility.

In this paper, a new method is proposed for solving forbidden state problems in non-ordinary controlled Petri nets (NCPNs) with uncontrollable transitions. Using a precedence subnet and a boundary subnet with decision-free properties, the behavior of markings are analyzed structurally. An efficient algorithm is presented for calculating the number of total tokens in forbidden places reachable from a marking. This paper derives necessary and sufficient conditions for identifying admissible markings and boundary markings in terms of the precedence subnet and the boundary subnet.

This paper presents an efficient method to derive the first passage time of an extended stochastic Petri net by simple algebraic operations. The reachability graph is derived from an extended stochastic Petri net, and then converted to a timed stochastic state machine which is a semi-Markov process. The mean and the variance of the first passage time are derived by algebraic manipulations with the mean and the variance of the transition time, and the transition probability for each transition in the state machine model. For the derivation, three reduction rules are introduced on the transition trajectories in a well-formed regular expression. An efficient algorithm is provided to automate the suggested method.