Forbidden state control synthesis for timed Petri net models

Abstract

Complex, computer controlled plants can be analyzed efficiently by reducing the very large state space to a finite state space, using abstraction. At the same time the model can be decomposed in smaller components. Automata can be used as models for — components of — such discrete event systems. Proper behaviour of the system means that the global state of the system never reaches forbidden subsets, or equivalently, that certain forbidden sequences of transitions between states never occur. Ramadge and Wonham [6] developed a framework for control of discrete event systems. The state evolution can be constrained by blocking some controllable transitions. For a class of untimed Petri nets Holloway and Krogh [4] developed an efficient algorithm for synthesizing maximally permissive control laws, guaranteeing that the state never reaches some forbidden set. It turns out that this maximally permissive control law only depends on the marking of places in a subnet of the Petri net, and that control action is only required at transitions at the boundary of this same subnet. This subnet is called the influencing net [1, 4, 7].

The results presented in this paper have been obtained within the framework of the Belgian Program on Interuniversity Attraction Poles, initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility rests with its authors. R.K. Boel is supported by the Flemish Foundation for Scientific Research as Senior Research Associate.