## ABSTRACT

Behavioral permissiveness is an important criterion to evaluate the performance of a Petri net supervisor. A behaviorally optimal Petri net supervisor implies that the supervisor does not prohibit any safe state but forbid all unsafe states. In this case, the controlled system can utilize the resources at anytime if the utilization does not lead to an unsafe state. A behaviorally optimal supervisor usually implies high utilization of the resources in AMSs. Thus, it is interesting and significant to achieve the goal of optimal control (Ghaari et al., 2003; Piroddi et al., 2008, 2009). However, most of the existing deadlock prevention policies are suboptimal (Fanti and Zhou, 2004, 2005; Huang et al., 2001; Jeng and Xie, 2005; Li and Zhou, 2004, 2006; Uzam and Zhou, 2006; Viswanadham et al., 1990). Usually, a behaviorally optimal supervisor is called a maximally permissive supervisor.