@@ -165,7 +165,7 @@ use functions and maximizes the utility $U(\tau, T)$.

Since the perfect use function $u(t)$ was chosen with knowledge of all harvested energy for all times, the battery level will drop to 0\% only at times, when the harvesting functions starts delivering more energy than we currently use. \\

The energy consumption will then be chosen, such that the battery is full, when the harvesting function is decreasing, thus after the battery is fully charged, the use function should decrease. \\

\subsection{Finite Horizon Control}

\subsubsection{Finite Horizon Control}

To find an optimal use function.\\

We do not know the future energy harvesting correctly. To deal with that, we use a estimation of the future harvested energy $\tilde{p}(\tau)$\\