Computation of State Avoidance Control for In nite State

In this paper we study supervisory control of discrete event systems using state variables for representation and speciication. The motivation is two fold: rstly, a state variable representation allows a concise characterization of systems with innnitely many states, and secondly, state variable speciication allows characterization of qualitative properties of general nondeterministic systems. An assignment program consisting of state variables and a nite set of conditional assignment statements is used for representing a discrete event system, and a set of forbidden states is used for representing a control spec-iication. Although the state avoidance control of innnite state systems has been studied in literature, there is little work on computation of supervisors for general innnite state systems (except for certain classes of Petri nets). The contribution of this paper is to show that the supervisory control problem in such settings reduces to that of solving arithmetic equations. In the special case when the system can be represented as a vector addition system or equivalently, a Petri net, and the set of forbidden states is a right-closed set we provide techniques for maximally permissive supervision.