Distributed parameter methods for moving sensor networks in unison

We incorporate optimization results of spatially distributed systems to design the optimal spatiotemporal allocation of sensors moving in unison. By viewing the positioning of the mobile agents within a network as the discrete spatial representation of the density of an equivalent single mobile sensor, the problem of motion-in-unison is converted into the problem of obtaining the spatial distribution and motion of a single sensing device. The single mobile sensor is integrated within the process at which it interacts with, and then the optimal sensor distribution uses the covariance of the associate statistical estimator of the process as a performance metric. To minimize the computational and algorithmic complexity of viewing the optimal estimator with a variable lower time limit of a cost-to-go, we consider instead a hybrid equivalent, wherein the time horizon is decomposed into a sequence of disjoint integrals mimicking model predictive control.