An extended model of Petri net and application in DEDS

Abstract

The logic supervisor and structural supervisor based on controlled Petri net are difficult to model discrete event dynamic systems (DEDS) when the initial system state is uncertain or illegal. An extended Petri net is provided to solve the problem. The net (Jade-structure) just adjusts basic element of Petri net, and is adopted to model the open loop feedback control systems. The model of DEDS based on Jade-structure, is controlled by control conditions and makes system run in legal state space. The supervisor of Jade-structure based on system state (M-Jade) and the other supervisor based on the transition set of Jade-structure (T-Jade) are formally described, and M-Jade is extended to three extended models. The first extended model based on the subset of the place set, judges part of system current state and adjusts system state. The second based on the restriction inequations set of system state, judges the system current state equation and adjusts system state. The last adjusts system state by negative vectors. The controlled Jade-structure (C-Jade) based on T-Jade and M-Jade, models to DEDS with controlled places and uncontrolled places. When DEDS sets uncertain initial state, the controlled structure uses a set of restriction in-equations to avoid system running into illegal state place without computing the whole state place. If system meets abnormities, C-Jade structure makes system run back to permitted state place by negative vectors. And negative vectors and restriction in-equations also can be set by judging the marking of place subset. An example was modeled and validated by C-Jade, and the characteristics of C-Jade were discussed.