On the choice of suboptimal monitors for supervisory control of Petri nets

Recent results in the literature have provided an efficient control synthesis technique for the problem of enforcing generalized mutual exclusion constraints on place/transition nets. With this technique both the plant and the controller are described by Petri nets in order to have an useful linear algebraic model for control analysis and synthesis. The synthesis is not computation demanding since it involves only matrix multiplications. Moreover the method has been shown to be maximally permissive in the case of controllable specifications, otherwise the controller may be suboptimal and its structure may not be unique. This paper investigates on and provides an algorithm to compute these control structures and two criteria of suboptimality.