Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators

In this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints (stair-GMECs) is defined. A stair-GMEC can be represented by an inequality whose left-hand is a linear combination of floor functions. Stair-GMECs have a higher modeling power than classical GMECs and can model legal marking sets that cannot be defined by OR-AND GMECs. We propose two algorithms to enforce a stair-GMEC as a closed-loop net, in which the control structure is composed by a residue counter, remainder counters, and duplicate transitions. We also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net. This approach can be applied to both bounded and unbounded nets. Several examples are proposed to illustrate the approach. Published as: [Z.Y. Ma, Z.W. Li, A. Giua, “Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators,” Automatica, Vol. 74, pp. 238-246, 2016] DOI: 10.1016/j.automatica.2016.07.042. Ziyue Ma is with School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China, and also with Dipartimento di Ingegneria Elettrica ed Elettronica, Università degli Studi di Cagliari, Cagliari, Italy (email: [email protected]). Zhiwu Li is with Institute of Systems Engineering, Macau University of Science and Technology, Taipa, Macau (email: [email protected], [email protected]). Alessandro Giua is with Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LSIS UMR 7296, Marseille 13397, France (email: [email protected]) and DIEE, University of Cagliari, Cagliari 09124, Italy (email: [email protected]). This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61374068, 61472295, the Recruitment Program of Global Experts, the ShaanXi Huashan Scholars, and the Science Technology Development Fund, MSAR, under Grant No. 078/2015/A3.