## 1 Introduction  
A typical example of discrete event systems is an automated manufacturing system (AMS) [1, 2]. It enables various product types to be entered at discrete times by sharing resources like machines, automatic controlled vehicles, automated tools, robots, and buffers at asynchronous or simultaneous operations. AMSs have to cope with unexpected and rapid market changes on a competitive global market. They must make rapid modifications to their software and hardware to meet these dynamic changes. This requirement cannot, however, be satisfied successfully with traditional automated manufacturing systems, which require large capital investments. Reconfigurable manufacturing systems have now been developed to deal with those drawbacks in traditional automated manufacturing systems [3, 4, 5]. Reconfigurable manufacturing systems are a new kind of production systems that are randomly and dynamically configured in real time. Such configurations involve processing rework and failures, adding new products and machines, and adding new handling device. In RMSs, a set of system resources can be used to process each component according to a specific process sequence. This sharing of resources, however, may lead to deadlocks, and some operations can therefore remain incomplete. Therefore, dealing with deadlock problem is critical for RMSs. Petri nets (PNs) are widely used for the scheduling, deadlock analysis and control in AMSs as graphical and mathematical modelling tools [6; 7; 8; 9; 10; 11; 12; 13; 14]. They can be used to describe characteristics and behaviors of AMSs such as synchronization, concurrency, conflict, causal dependence, and sequencing. Petri nets can be used for behavioral features, for example boundedness and liveness [15; 16]. From a technical point of view, several policies based on Petri nets have been proposed. These policies are based on three strategies: (i) deadlock detection and recovery, (ii) deadlock avoidance, and (iii) deadlock prevention [15; 17]. Most of these policies have proposed deadlock control in Petri nets through structural analysis [6; 18] and reachability graph analysis [19; 20; 21]. In addition, three criteria to evaluate and construct an AMS supervisor have been proposed, namely behavioral permissiveness, computational complexity, and structural complexity [15; 22]. Recently, several approaches have been adapted to deal with dynamic changes in manufacturing systems [7; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. They primarily concentrate in two directions: direct and indirect. Direct approaches provide modification mechanisms or particular rules for system structure configurations, while indirect approaches typically import additional mechanisms for system reconfiguration specifications. The event-condition-action (ECA) paradigm is developed by [PERSON] et al. [30] for the design of reconfigurable logic controllers. Their research has demonstrated that the reconfiguration process is highly dependent on the modularity level of the logical control system and that not all \"modular\" structures can be reconfigured. For a class of discrete event systems (DESs), [PERSON] et al. [26] presented a reconfiguration approach for their control specifications, subject to linear constraint. This approach is suited to systems such as hospital management systems and can be reconfigured in non-real time. In order to evaluate and improve the performance of the control architecture, [PERSON] et al. [27] developed a real-time reconfigurable supervised control architecture for large manufacturing systems. A model-based control design for reconfigurable manufacturing systems is developed by [PERSON] and [PERSON] [28] through state transition diagrams and general graph representation taking into account configuration and reuse of design data.