This paper addresses an application of the potential game theory to a power-aware mobile sensor coverage problem where each sensor tries to maximize a probability of target detection in a convex mission space. The probability of target detection depends on a sensing voltage of each mobile sensor as well as its current position. While a higher sensing voltage improves the target detection probability, this requires more power consumption. In this paper, we assume that mobile sensors have different sensing capabilities of detecting a target and they can adaptively change sensing areas by adjusting their sensing voltages. We consider an objective function to evaluate a trade-off between improving the target detection probability and reducing total power consumption of all sensors. We represent a sensing voltage and a position of each mobile sensor using a barycentric coordinate over an extended strategy space. Then, the sensor coverage problem can be formulated as a potential game where the power-aware objective function and the barycentric coordinates correspond to a potential function and players' mixed strategies, respectively. It is known that all local maximizers of a potential function in a potential game are equilibria of replicator dynamics. Based on this property of potential games, we propose decentralized control for the power-aware sensor coverage problem such that each mobile sensor finds a locally optimal position and sensing voltage by updating its barycentric coordinate using replicator dynamics.

A new method for interpolating boundary function values and first derivatives of a triangle is presented. This method has a relatively simple construction and involves no compatibility constraints. The polynomial precision set of the interpolation function constructed includes all the cubic polynomial and less. The testing results show that the surface produced by the proposed method is better than the ones by weighted combination schemes in both of the fairness and preciseness.