Energy-saving optimization is very important for various engineering problemsrelated to modern distributed systems. We consider here a control problem for awireless sensor network with a single time server node and a large number ofclient nodes. The problem is to minimize a functional which accumulates clocksynchronization errors in the clients nodes and the energy consumption of theserver over some time interval $[0,T]$. The control function $u=u(t)$, $0\lequ(t)\leq u_{1}$, corresponds to the power of the server node transmittingsynchronization signals to the clients. For all possible parameter values wefind the structure of optimal trajectories. We show that for sufficiently large$u_{1}$ the solutions contain singular arcs.
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