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 A Comparative Study of Redundant Constraints Identification Methods in Linear Programming Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Paulraj S. ◽  
Sumathi P.
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Linear Functions ◽  
Redundant Constraints ◽  
Computer Scientists ◽  
Constraints Solving ◽  
Linear Programming Problems

The objective function and the constraints can be formulated as linear functions of independent variables in most of the real-world optimization problems. Linear Programming (LP) is the process of optimizing a linear function subject to a finite number of linear equality and inequality constraints. Solving linear programming problems efficiently has always been a fascinating pursuit for computer scientists and mathematicians. The computational complexity of any linear programming problem depends on the number of constraints and variables of the LP problem. Quite often large-scale LP problems may contain many constraints which are redundant or cause infeasibility on account of inefficient formulation or some errors in data input. The presence of redundant constraints does not alter the optimal solutions(s). Nevertheless, they may consume extra computational effort. Many researchers have proposed different approaches for identifying the redundant constraints in linear programming problems. This paper compares five of such methods and discusses the efficiency of each method by solving various size LP problems and netlib problems. The algorithms of each method are coded by using a computer programming language C. The computational results are presented and analyzed in this paper.

scholarly journals A Survey of Elementary Object Systems

10.29007/dqbd ◽  
2018 ◽  
Author(s):  
Michael Köhler-Bußmeier
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Computational Effort ◽  
State Machines ◽  
Restricted Class ◽  
Turing Complete ◽  
Relationship Of ◽  
The Relationship ◽  
Linear Invariants

This contribution presents the formalism of ElementaryObjectSystems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. One central aim of this contribution is to compile all our previous works ded- icated to certain aspects of Eos together with recent yet unpublished results within one self-contained presentation. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. In this work we study the relationship of Eos to existing Petri net formalisms. It turns out that Eos are more powerful than classical p/t nets which is demonstrated by the fact that e.g. reachability and liveness become undecidable problems for Eos. Despite these undecidability results other properties can be extended to Eos using a monotonicity argument similar to that for p/t nets. Also linear algebraic techniques, especially the theory of linear invariants and semiflows, can be extended in an appropriate way. The invariant calculus for Eos even enjoys the property of compositionality, i.e. invariants of the whole system can be composed of invariants of the object nets, which reduces the computational effort. To obtain a finer level of insight we also studied several classes like pure, minimal, or semi-bounded Eos. Among these variants the subclass of generalised state machines is worth mentioning since it combines the decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.

scholarly journals Single Controller-Based Colored Petri Nets for Deadlock Control in Automated Manufacturing Systems

Processes ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 21 ◽  
Author(s):  
Husam Kaid ◽  
Abdulrahman Al-Ahmari ◽  
Zhiwu Li ◽  
Reggie Davidrajuh
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Manufacturing Systems ◽  
Colored Petri Nets ◽  
Second Step ◽  
Deadlock Prevention ◽  
Automated Manufacturing ◽  
Automated Manufacturing Systems ◽  
Control Approach ◽  
Single Controller

Deadlock control approaches based on Petri nets are usually implemented by adding control places and related arcs to the Petri net model of a system. The main disadvantage of the existing policies is that many control places and associated arcs are added to the initially constructed Petri net model, which significantly increases the complexity of the supervisor of the Petri net model. The objective of this study is to develop a two-step robust deadlock control approach. In the first step, we use a method of deadlock prevention based on strict minimal siphons (SMSs) to create a controlled Petri net model. In the second step, all control places obtained in the first step are merged into a single control place based on the colored Petri net to mark all SMSs. Finally, we compare the proposed method with the existing methods from the literature.

scholarly journals Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yen-Liang Pan ◽  
Yi-Sheng Huang ◽  
Yi-Shun Weng ◽  
Weimin Wu ◽  
MuDer Jeng
Keyword(s):  
Linear Programming ◽  
Petri Net ◽  
Flexible Manufacturing ◽  
Manufacturing Systems ◽  
Computational Cost ◽  
Deadlock Prevention ◽  
Prevention Policy ◽  
Linear Programming Problems ◽  
Control Methodology ◽  
State Separation

Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches.

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