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The paper proposes the novel concurrency and sequentiality analysis techniques of a cyber-physical system specified by a safe Petri net. The presented methods are based on the hypergraph theory and apply computation of exact transversals in a c-exact hypergraph. The proposed techniques are supported by adequate algorithms, theorems, and proofs. Furthermore, the presented methods are illustrated by a case-study example of a real-life cyber-physical system. Finally, the results of the conducted experiments are shown and discussed. INDEX TERMS Petri nets, concurrent and sequential relations, hypergraphs, cyber-physical systems.

This paper proposes a Petri-net-based specification of cyber-physical systems dedicated to the control of a direct matrix converter with space vector modulation (SVM) and transistor commutation. The technique employed is further applied for hardware implementation in a programmable logic device [namely, field-programmable gate array (FPGA)]. Contrary to the traditional SVM computation methods, concurrency aspects of the digital devices are highly utilized in the presented solution. Therefore, the hardware system is specified by a live and safe Petri net, which is based on the parallelism. Moreover, such a specification can be easily analyzed and verified against the structural properties in order to avoid formal errors and prototyping mistakes (such as deadlocks or non-reachable states). The proposed idea is illustrated by a case-study example of the real prototype of the SVM algorithm. The system has been specified by a live and safe Petri net, analyzed, verified, and finally implemented in the FPGA device. The obtained results of the physical implementation are presented and discussed.

Abstract. The paper deals with the application of the hypergraph theory in selection of State Machine Components (SM-Components) of Petri nets [1,2].As it is known, Petri nets are widely used for modeling of concurrency processes. However, in order to implement the concurrent automaton, an initial Petri net ought to be decomposed into sequential automata (SM-Components), which can be easily designed as an Finite-State-Machine (FSM) or Microprogrammed Controller [3]. The last step of the decomposition process of the Petri nets is selection of SM-Components. This stage is especially important because it determines the final number of sequential automata. In the article we propose a new idea of SM-Components selection. The aim of the method is reduction of the computational complexity from exponential to polynomial. Such a reduction can be done if the selection hypergraph belongs to the exact transversal hypergraphs (xt-hypergraphs) class. Since the recognition and generation of the first transversal in the xt-hypergraphs are both polynomial, the complete selection process can be performed in polynomial time. The proposed ideas are an extension of the concept presented in [1]. The proposed method has been verified experimentally. The conducted investigations have shown that for more than 85% of examined Petri nets the selection process can be done via xt-hypergraphs.

In this paper, we study selected aspects of determinism in the control part of a cyber-physical system (CPS) that is specified by a Petri net-based model. In particular, the control interpreted Petri nets (CIPNs) are applied, which are an extension of the ordinary Petri nets, supplemented by signals (related to sensors and actuators) that permit communication with the environment. The notions of weak and strong determinism in a system described by a CIPN are introduced in the paper. The proposed concepts are supported by formal definitions and theorems. Moreover, a novel modelling methodology for a deterministic system specified by a CIPN is proposed. The presented solutions are illustrated by a case study example of a real-life cyber-physical system. Finally, the results of experimental verification of the proposed determinism-based techniques are demonstrated and discussed.