  We consider an energy harvesting information update system where a sensor is
allowed to choose a transmission mode for each transmission, where each mode
consists of a transmission power-error pair. We also incorporate the battery
phenomenon called battery recovery effect where a battery replenishes the
deliverable energy if kept idle after discharge. For an energy-limited age of
information (AoI) system, this phenomenon gives rise to the interesting
trade-off of recovering energy after transmissions, at the cost of increased
AoI. Considering two metrics, namely peak-age hitting probability and average
age as the worst-case and average performance indicators, respectively, we
propose a framework that formulates the optimal transmission scheme selection
problem as a Markov Decision Process (MDP). We show that the gains obtained by
considering both battery dynamics and adjustable transmission power together
are much higher than the sum gain achieved if they are considered separately.
We also propose a simple methodology to optimize the system performance taking
into account worst-case and average performances jointly.
