On the enforcement of a class of nonlinear constraints on Petri nets

This paper focuses on the enforcement of nonlinear constraints in Petri nets. First, a supervisory structure is proposed for a nonlinear constraint. The proposed structure consists of added places and transitions. It controls the transitions in the net to be controlled only but does not change its states since there is no arc between the added transitions and the places in the original net. Second, an integer linear programming model is proposed to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same control performance as the nonlinear one. By using a place invariant based method, the obtained linear constraints can be easily enforced by a set of control places. The control places consist to a supervisor that can enforce the given nonlinear constraint. On condition that the admissible markings space of a nonlinear constraint is non-convex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint. Finally, a number of examples are provided to demonstrate the proposed approach. Published as: Y.F. Chen, Z.W. Li, K. Barkaoui, A. Giua, ”On the Enforcement of a Class of Nonlinear Constraints on Petri Nets,” Automatica, Vol. 55, pp. 116-124, 2015. DOI: 10.1016/j.automatica.2015.02.014. *YuFeng Chen is with the School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China, and also with Cedric Lab and Computer Science Department, Conservatoire National des Arts et Métiers, Paris 75141, France (e-mail: [email protected]). ZhiWu Li is with Institute of Systems Engineering, Macau University of Science and Technology, Macau, School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China, and Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia (e-mail: [email protected]). Kamel Barkaoui is with Cedric Lab and Computer Science Department, Conservatoire National des Arts et Métiers, Paris 75141, France (e-mail: [email protected]). Alessandro Giua is with Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LSIS UMR 7296, 13397, Marseille, France, DIEE, University of Cagliari, 09123 Cagliari, Italy, and School of Electro-Mechanical Engineering, Xidian University, Xi’an 710071, China (emails: [email protected] and [email protected]).