Worst-case performance of a mobile sensor network under individual sensor failure

In this paper, we consider the problem of worst-case performance by a mobile sensor network (MSN) when some of the nodes in the network fail. We formulate the problem as a game in which some subset of the nodes act in an adversarial manner, choosing their motion strategies to maximally degrade overall performance of the network as a whole. We restrict our attention in the present paper to a target detection problem in which the goal is to minimize the probability of missed detection. We use a partitioned cost function that is minimized when each sensor executes a motion strategy given by Lloyd's algorithm (i.e., each agent moves toward the centroid of its Voronoi partition at each time instant), and when the probability of missed detection for each functioning sensor increases with the distance between sensor and target for correctly functioning sensors; adversarial nodes in the network are unable to detect the target, and move to maximally increase the probability of missed detection by the properly functioning sensors. We pose the problem as a multi-stage decision process, and use forward dynamic programming over a finite horizon to numerically compute optimal strategies for the adversaries. We compare the resulting strategies to a greedy algorithm, providing both system trajectories and evolution of the probability of missed detection during execution.