In this paper, we consider the on-line estimation of optimal current subsequences in Partially Observable Untimed Petri Nets. Applying the counter approach classically used in max-plus algebra for Timed Petri nets, the idea is to exploit the assumption of a non immediate consumption of the tokens for each place which introduces an order of precedence between events. The approach can estimate a global price depending on the costs and gains provided by the tasks. The estimation of optimal sequences is based on the determination of a time horizon necessary to describe the sequences. The estimation is relevant to a step defined by two successive occurrences of observable transition firings. We show that the approach can consider any optimization problem if the dates of the observations are known or, if a guaranteed horizon can be computed which is always possible when the unobservable subnet satisfies a weak assumption close to the structural boundedness (relaxed structurally boundedness). As the technique avoids the generation of sets, the approach does not depend on their cardinalities and is numerically efficient.

在本文中，我们考虑了部分可观测的非定时Petri网中最优电流子序列的在线估计。将经典的最大加数代数中使用的计数器方法应用于定时在Petri网中，该想法是针对每个位置使用令牌的非立即消耗的假设，该假设在事件之间引入了优先顺序。该方法可以根据任务提供的成本和收益来估算全球价格。最佳序列的估计是基于确定描述序列所需的时间范围的。该估计与由两次连续出现的可观察到的过渡点火所定义的步骤有关。我们表明，如果已知观测日期，或者如果可以计算出保证范围，则该方法可以考虑任何优化问题。当无法观察的子网满足接近结构边界（松弛结构边界）的弱假设时，保证地平线总是可能的。由于该技术避免了生成集，