State Avoidance Control for In nite State

In this paper we study supervisory control of discrete event systems using state variables for representation and speci cation. The motivation is two fold: rstly, a state variable representation allows a concise characterization of systems with in nitely many states, and secondly, state variable speci cation 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 speci cation. The control synthesis problem is undecidable in the general setting. However, in the special case when a single uncontrollable event is present, we show that the problem of computing a maximally permissive supervisor reduces to that of solving an arithmetic equation. Also, in another 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. This generalizes the existing results on controlled vector addition systems.