Optimal visiting schedule search for persistent monitoring of a finite set of targets
Xi Yu, Sean B. Andersson, Nan Run Zhou, Christos G. Cassandras · 2018
This paper considers the design of a periodic schedule for an agent moving around a finite number of targets, repeatedly visiting them to collect information about the target. The design is composed of two parts: 1) determining the sequence of targets that the agents should visit, and 2) selecting the amount of time that the agents should spend at each target. We translate the latter into an optimal control problem to determine switching conditions such that the agents will dwell at the target until these conditions are met. Under a mild assumption, we show that the system falls into a steady cycle when constant switching conditions are provided to the system, and find a simple choice of switching conditions that optimizes particular metrics of the persistent monitoring problem, including minimizing the duration of the period of the repeating sequence and the peak value of the uncollected information at the targets. We then use this condition to narrow the search for an optimal sequence from an infinite number of possible sequences to a finite (though possibly very large) number by determining an upper bound on the number of visits at any given target. Finally, we develop an algorithm for modifying any given sequence to reduce the average information level summed across all the targets.