Modular supervisory control may lead to conflicts among the modular supervisors for large-scale discrete event systems. The existing methods for ensuring nonblocking control of modular supervisors either exploit favorable structures in the system model to guarantee the nonblocking property of modular supervisors or employ hierarchical model abstraction methods for reducing the computational complexity of designing a nonblocking coordinator. The nonblocking modular control problem is, in general, NP-hard. This study integrates supervisory control theory and a model-based deep reinforcement learning method to synthesize a nonblocking coordinator for the modular supervisors. The deep reinforcement learning method significantly reduces the computational complexity by avoiding the computation of synchronization of multiple modular supervisors and the plant models. The supervisory control function is approximated by the deep neural network instead of a large-sized finite automaton. Furthermore, the proposed model-based deep reinforcement learning method is more efficient than the standard deep Q network algorithm.

Fuzzy Petri nets (FPNs) are a vital modeling technique for the construction of knowledge-based systems, which have been commonly used in many fields, such as fault diagnosis, risk assessment, workflow management, and disassembly process planning. However, the conventional FPNs have been blamed for the following reasons: 1) the representation parameters in FPNs cannot precisely model experts' experience since it is difficult to manage the fuzziness and randomness of knowledge assessments simultaneously, and 2) the weight coefficients in the existing approximate reasoning algorithms are hardly enough to reflect the associated weights of reordered places. In response, we propose a new type of FPNs, called cloud reasoning Petri nets (CRPNs) based on the concept of interval clouds and the hybrid averaging operator. The cloud production rules in a knowledge-based system are modeled by CRPNs, where the truth degrees of places, the certainty factors of rules, and the thresholds of transitions are represented by interval clouds. Moreover, a matrix operation-based reasoning algorithm is proposed to improve the efficiency of calculating final truth degrees, in which both local and ordered weight coefficients are taken into consideration. Finally, a practical example concerning a power system is provided to demonstrate the usefulness and advantages of the proposed CRPN model.