  This paper studies an online algorithm for an energy harvesting transmitter,
where the transmission (completion) time is considered as the system
performance. Unlike the existing online algorithms which more or less require
the knowledge on the future behavior of the energy-harvesting rate, we consider
a practical but significantly more challenging scenario where the
energy-harvesting rate is assumed to be totally unknown. Our design is
formulated as a robust-optimal control problem which aims to optimize the
worst-case performance. The transmit power is designed only based on the
current battery energy level and the data queue length directly monitored by
the transmitter itself. Specifically, we apply an event-trigger approach in
which the transmitter continuously monitors the battery energy and triggers an
event when a significant change occurs. Once an event is triggered, the
transmit power is updated according to the solution to the robust-optimal
control problem, which is given in a simple analytic form. We present numerical
results on the transmission time achieved by the proposed design and
demonstrate its robust-optimality.
