Decision on Maximal Permissiveness of Linear Constraints via Structural Analysis of a Subclass of Petri Nets

2019 ◽  
pp. 1-12
Author(s):  
HeFeng Chen ◽  
NaiQi Wu ◽  
ZhiWu Li ◽  
Ting Qu
Keyword(s):  
Structural Analysis ◽  
Petri Nets ◽  
Linear Constraints ◽  
Maximal Permissiveness

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.

Approach for Transforming Linear Constraints on Petri Nets

2011 ◽  
Vol 56 (12) ◽  
pp. 2751-2765 ◽  
Author(s):  
Jiliang Luo ◽  
Kenzo Nonami
Keyword(s):  
Petri Nets ◽  
Linear Constraints

Structural Controller for Logical Expression of Linear Constraints on Petri Nets

2020 ◽  
Vol 65 (1) ◽  
pp. 397-403 ◽  
Author(s):  
Jiliang Luo ◽  
Weimin Wu ◽  
Mengchu Zhou ◽  
Hui Shao ◽  
Kenzo Nonami ◽  
...  
Keyword(s):  
Petri Nets ◽  
Linear Constraints ◽  
Logical Expression

Petri Net Supervisory Method for Linear Constraints and its Applications to Flexible Manufacturing Systems

2013 ◽  
pp. 20-35
Author(s):  
Jiliang Luo
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Flexible Manufacturing System ◽  
Linear Constraints ◽  
Supervisor Synthesis ◽  
Synthesis Procedure

An algorithm is proposed to equivalently transform original linear constraints on Petri nets, where the uncontrollable subnets are forward-concurrent free nets, into admissible ones. Consequently, this algorithm can be used to design both efficient and optimal supervisors for enforcing linear constraints on Petri nets since the problem on how to enforce admissible constraints has been well solved. Further, the supervisor synthesis procedure is presented using this algorithm. Lastly, it is illustrated by an example where an optimal supervisor is designed for a flexible manufacturing system.

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