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Sensor Selection for Structural Observability in Discrete Event Systems Modeled by Petri Nets

机译：Petri网建模的离散事件系统中结构可观察性的传感器选择

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摘要

This paper studies optimal sensor selection in discrete event systems modeled by partially observed Petri nets. The goal is to place a minimum number of sensors while maintaining structural observability, i.e., the ability to uniquely determine the system state at any given time step based on sensor information up to that time step, knowledge of the system model, and an arbitrary but known initial state. The problem is important because the majority of existing control schemes for Petri nets rely on complete knowledge of the system state at any given time step. To simplify the problem, we consider two subproblems: the optimal place sensor selection (OPSS) problem and the optimal transition sensor selection (OTSS) problem. The OPSS problem is shown to be computationally hard by establishing that the corresponding decision problem is ${cal NP}$ -complete. For this reason, we first reduce the problem to the linear integer programming problem, which can be solved optimally using existing linear integer programming solvers (at least for small problem instances), and then propose two heuristic algorithms to approximate its solution with polynomial complexity. Simulations suggest that the two proposed heuristics run faster and can find reasonably good solutions when compared to optimal methods that are based on linear integer programming solvers. Unlike the OPSS problem, the OTSS problem is solvable with polynomial complexity.
机译：本文研究了由部分观测到的Petri网建模的离散事件系统中的最佳传感器选择。目标是在保持结构可观察性的同时放置最少数量的传感器，即具有基于该时间步长之前的传感器信息，系统模型知识以及任意但任意的唯一确定时间步长的系统状态的能力。已知的初始状态。这个问题很重要，因为大多数现有的Petri网控制方案都依赖于在任何给定时间步长上对系统状态的完整了解。为了简化该问题，我们考虑了两个子问题：最佳位置传感器选择（OPSS）问题和最佳过渡传感器选择（OTSS）问题。通过确定相应的决策问题是$ {cal NP} $ -complete，表明OPSS问题在计算上比较困难。因此，我们首先将问题简化为线性整数规划问题，可以使用现有的线性整数规划求解器（至少对于小问题实例）以最佳方式解决该问题，然后提出两种启发式算法以多项式复杂度近似求解。仿真表明，与基于线性整数规划求解器的最佳方法相比，所提出的两种启发式算法运行速度更快，并且可以找到相当好的解决方案。与OPSS问题不同，OTSS问题可通过多项式复杂度来解决。

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