Control of discrete event systems with their dynamics and legal behavior specified by Petri nets

In the paper, we study the supervisory control (event string avoidance control) of discrete event systems (DES´s) of which the physical possible behavior is modelled by an ordinary Petri net and legal behavior is specified by a deterministic labelled Petri net. The advantage of taking a Petri net as the specification of the legal behavior of a DES is that it can both specify the desired interleaving behavior and the concurrent execution constraints of the DES. The problem of the paper is to synthesize a feedback control policy for a DES such that the behavior of the DES under the control of the control policy satisfies a given behavior specification. To solve the problem, we first transform it into an equivalent state feedback control (state avoidance control) problem of an induced system with specific permissive state set. For the permissive state set, under a weak assumption that the underlying system can not occur any infinite uncontrollable event sequence, we propose a method to calculate the supremal control-invariant subset of the permissive state set, and then give a minimally restrictive state feedback control policy allowing maximal concurrency for the induced system