  We consider a system where multiple sensors communicate timely information
about various random processes to a sink. The sensors share orthogonal
sub-channels to transmit such information in the form of status update packets.
A central controller can control the sampling actions of the sensors to
trade-off between the transmit power consumption and information freshness
which is quantified by the Age of Information (AoI). We jointly optimize the
sampling action of each sensor, the transmit power allocation, and the
sub-channel assignment to minimize the average total transmit power of all
sensors subject to a maximum average AoI constraint for each sensor. To solve
the problem, we develop a dynamic control algorithm using the Lyapunov
drift-plus-penalty method and provide optimality analysis of the algorithm.
According to the Lyapunov drift-plus-penalty method, to solve the main problem
we need to solve an optimization problem in each time slot which is a mixed
integer non-convex optimization problem. We propose a low-complexity
sub-optimal solution for this per-slot optimization problem that provides
near-optimal performance and we evaluate the computational complexity of the
solution. Numerical results illustrate the performance of the proposed dynamic
control algorithm and the performance of the sub-optimal solution for the
per-slot optimization problems versus the different parameters of the system.
The results show that the proposed dynamic control algorithm achieves more than
$60~\%$ saving in the average total transmit power compared to a baseline
policy.
