We investigate the problem of optimally observing a finite set of targets using a mobile agent over an infinite time horizon. The agent is tasked to move in a network-constrained structure to gather information so as to minimize the worst-case uncertainty about the internal states of the targets. To do this, the agent has to decide its sequence of target-visits and the corresponding dwell-times at each visited target. For a given visiting sequence, we prove that in an optimal dwelling time allocation the peak uncertainty is the same among all the targets. This allows us to formulate the optimization of dwelling times as a resource allocation problem and to solve it using a novel efficient algorithm. Next, we optimize the visiting sequence using a greedy exploration process, using heuristics inspired by others developed in the context of the traveling salesman problem. Numerical results are included to illustrate the contributions.

我们研究了在无限时间范围内使用移动代理最佳地观察有限目标集的问题。代理的任务是在网络受限结构中移动以收集信息，以最大限度地减少目标内部状态的最坏情况不确定性。为此，代理必须决定其目标访问顺序和每个访问目标的相应停留时间。对于给定的访问序列，我们证明在最佳停留时间分配中，峰值不确定性在所有目标中是相同的。这使我们能够将停留时间的优化制定为资源分配问题，并使用一种新颖的高效算法来解决它。接下来，我们使用贪心探索过程优化访问顺序，使用在旅行商问题的背景下开发的受他人启发的启发式方法。包括数值结果以说明贡献。