Optimal Sensor Selection for Diagnosability Enforcement in Labeled Petri Nets
针对可能死锁的非可诊断标签Petri网，提出一种通过掩码标签函数增强可诊断性的策略，仅静默特定变迁的传感器，并用整数线性规划优化掩码函数，最后计算多故障K-可诊断系统的最小K值。
This article addresses the problem of optimal sensor selection for diagnosability enforcement of discrete event systems modeled with Petri nets. Given a nondiagnosable labeled Petri netlabeled Petri net (LPN) that may reach deadlocks, it can be enforced to be diagnosable by a novel systematic strategy through a mask labeling function. The proposed strategy employs a special nondeterministic finite automaton, namely, a simplified verifierSV, obtained from the original labeled Petri netLPN and a particular set of labels. Since we only need to silence sensors of some particular transitions rather than add or replace new sensors to transitions, it is more computationally efficient compared with other documented methods in the literature. In addition, we formulate and solve an integer linear programming problemILPP to optimize a set of given mask labeling functions. Finally, an algorithm is constructed to calculate the minimum value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula> for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula> -diagnosable system with multiple faults under the mask labeling function. Examples are presented to demonstrate the proposed method.