Abstract
In this paper, the optimal sensor location problem is first discussed for environmental monitoring of physical phenomena governed by some advection-diffusion partial-differential equations. In particular, the exact derivation of the observability Gramian of an advection-diffusion PDE is investigated. Based on the optimality criteria derived from this analysis, a conservation law governing the behavior of a crowd of mobile sensors is proposed to ensure convergence of the sensor density towards an optimal location. The monitoring of pollution on a 2D domain is the case study used throughout the paper to illustrate the effectiveness of the proposed approach.
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