Optimal Legal Firing Sequence of Petri Nets Using Linear Programming

2004 ◽  
Vol 5 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Ahmed Tarek ◽  
Noé Lopez-Benitez
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Legal Firing Sequence ◽  
Firing Sequence

Fault-tolerant tracking control of petri nets

2018 ◽  
Vol 66 (1) ◽  
pp. 30-40 ◽  
Author(s):  
Raphael Fritz ◽  
Ping Zhang
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Petri Net ◽  
Tracking Control ◽  
Fault Tolerant ◽  
Computational Effort ◽  
Control Approach ◽  
Sensor Actuator ◽  
Linear Programming Problems ◽  
Firing Sequence

Abstract In this paper, the fault-tolerant tracking control of petri nets is considered. The control aim is to steer a petri net in case of faults from an initial marking into a destination marking by an appropriate firing sequence. Sensor, actuator and process faults in the plant are modeled based on four types of faulty transitions. Depending on the characteristics of the faults, two approaches are proposed to handle the faults. The tracking control problem is realized by solving two integer linear programming problems. This two-step approach reduces the computational effort significantly. Faults are taken into account as constraints and by adapting the firing sequence. Finally, an example is given to illustrate the proposed fault-tolerant tracking control approach.

scholarly journals Equivalent Transformation of Nonlinear Constraints to Linear Constraints in Petri Nets

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
YuFeng Chen ◽  
Abdulrahman Al-Ahmari ◽  
Chi Tin Hon ◽  
NaiQi Wu
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Linear Constraints ◽  
Linear Programming Model ◽  
Equivalent Transformation ◽  
Nonlinear Constraints ◽  
Nonlinear Constraint ◽  
Integer Linear Programming Model

This paper focuses on the enforcement of nonlinear constraints in Petri nets. An integer linear programming model is formulated to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same admissible marking space as the nonlinear one does in Petri nets. The obtained linear constraints can be easily enforced to be satisfied by a set of control places with a place invariant based method. The control places make up a supervisor that can enforce the given nonlinear constraint. For a case that the admissible marking space decided by a nonlinear constraint is nonconvex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint with respect to the reachable markings. Finally, a number of examples are provided to demonstrate the proposed approach.

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