Optimization problems for WSNs: trade-off between synchronization errors and energy consumption
We discuss a class of optimization problems related to stochastic models of wireless sensor networks (WSNs). We consider a sensor network that consists of a single server node and m groups of identical client nodes. The goal is to minimize the cost functional which accumulates synchronization errors and energy consumption over a given time interval. The control function u(t) = (u1(t),...,um(t)) corresponds to the power of the server node transmitting synchronization signals to the groups of clients. We find the structure of extremal trajectories. We show that optimal solutions for such models can contain singular arcs.