  We study status updating under inexact knowledge about the battery levels of
the energy harvesting sensors in an IoT network, where users make on-demand
requests to a cache-enabled edge node to send updates about various random
processes monitored by the sensors. To serve the request(s), the edge node
either commands the corresponding sensor to send an update or uses the aged
data from the cache. We find a control policy that minimizes the average
on-demand AoI subject to per-slot energy harvesting constraints under partial
battery knowledge at the edge node. Namely, the edge node is informed about
sensors' battery levels only via received status updates, leading to
uncertainty about the battery levels for the decision-making. We model the
problem as a POMDP which is then reformulated as an equivalent belief-MDP. The
belief-MDP in its original form is difficult to solve due to the infinite
belief space. However, by exploiting a specific pattern in the evolution of
beliefs, we truncate the belief space and develop a dynamic programming
algorithm to obtain an optimal policy. Moreover, we address a multi-sensor
setup under a transmission limitation for which we develop an asymptotically
optimal algorithm. Simulation results assess the performance of the proposed
methods.
