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+\section{Conclusion}~\label{sec:conclusion}
+
+The aim of this project was to analyze the performance of \acrshort{gp} based
+controllers for use in longer lasting implementations, where differences in
+building behaviour become important compared to the initially available data.
+
+First, the performance of a classical \acrshort{gp} model trained on five days
+worth of experimental data was analyzed. Initially, this model performed very
+well both in one step ahead prediction and multi-step ahead simulation over new,
+unseen, data. With the change in weather, however, the model shifted from
+operating in the interpolated regions to the extrapolated regions of the initial
+weather data. In this scenario the model was unable to properly predict the
+\pdome\ behaviour and, as a consequence, the \acrshort{mpc} controller became
+unstable.
+
+Following that, several \acrshort{svgp} implementations were analyzed. The
+initial behaviour exhibited during parameter identification (cf.
+Section~\ref{sec:hyperparameters}) showed that the \acrshort{svgp} model was
+less capable of capturing building dynamics only based on the initial
+experimental dataset, possibly due to the \acrshort{elbo} approximation of the
+true log likelihood. While the \acrshort{svgp} model remained stable over the
+course of the 20-step ahead simulation, in the later steps it drifted much
+further from the real values than the equivalent \acrshort{gp} model.
+However, during the full-year simulation, this downside of the \acrshort{svgp}
+model was compensated by adding new data to the model training dataset each
+night at midnight. The model performance continuously improved over the course
+of the simulation, providing much better results overall.
+
+To better analyze the learning behaviour of the \acrshort{svgp} models, three
+variations of the initial \acrshort{svgp} were also simulated. The first
+variation consisted of training the initial model on only one day's worth of
+experimental data, as opposed to five days in the first case. This model was
+then regularly updated every night at midnight, just as the initial case. It
+turned out to provide very comparable results to the initial model, leading to
+the conclusion that the \acrshort{svgp} model can be initially deployed using
+much less training data, and it will still be able to correctly capture the
+building dynamics on subsequent updates.
+
+The second variation of the \acrshort{svgp} model was re-trained using a rolling
+window of five days' worth of data, in order to see the model's ability to learn 
+the proper building dynamics based only on closed-loop operation data. This
+model turned out to be unstable, and the full-year simulation showed that every
+time the model was trained using \textit{only} closed-loop operation data it
+turned unstable. This prompted a much higher excitation of the building for the
+following day, which in turn provided enough information to train a good model,
+that would last until this information was too old to be included in the
+training window, at which point the model would turn unstable again.
+
+In the last variation, the \acrshort{svgp} model was trained using a linear
+kernel. This model turned out to perform worse overall than the \acrshort{se}
+kernel model since it was unable to capture the more nuanced, non-linear
+behaviour of the building.
+
+
+\subsection{Further Research}~\label{sec:further_research}
+
+Section~\ref{sec:results} has presented and compared the results of a full-year
+simulation for a classical \acrshort{gp} model, as well as a few incarnations of
+\acrshort{svgp} models. The results show that the \acrshort{svgp} have much
+better performance, mainly due to the possibility of updating the model
+throughout the year. The \acrshort{svgp} models also present a computational
+cost advantage both in training and in evaluation, due to several approximations
+shown in Section~\ref{sec:gaussian_processes}.
+
+Focusing on the \acrlong{gp} models, there could be several ways of improving
+its performance, as noted previously: a more varied identification dataset and
+smart update of a fixed-size data dictionary according to information gain,
+could mitigate the present problems.
+
+Using a Sparse \acrshort{gp} without replacing the maximum log likelihood
+with the \acrshort{elbo} could improve performance of the \acrshort{gp} model at
+the expense of training time.
+
+An additional change that could be made is inclusion of the most amount of prior
+information possible through setting a more refined kernel, as well as adding
+prior information on all the model hyperparameters when available. This approach
+however goes against the `spirit' of black-box approaches, since significant
+insight into the physics of the plant is required in order to properly model and
+implement this information.
+
+On the \acrshort{svgp} side, several changes could also be proposed, which were
+not properly addressed in this work. First, the size of the inducing dataset was
+chosen experimentally until it was found to accurately reproduce the manually
+collected experimental data. In order to better use the available computational
+resources, this value could be found programmatically in a way to minimize
+evaluation time, while still providing good performance. Another possibility is
+the periodic re-evaluation of this value when new data comes in, since as more
+and more data is collected the model becomes more complex, and in general more
+inducing locations could be necessary to properly reproduce the training data.
+
+Finally, none of the presented controllers take into account occupancy rates or
+adapt to possible changes in the real building, such as adding or removing
+furniture, deteriorating insulation and so on. The presented update methods only
+deals with adding information on behaviour in different state space regions, i.e
+\textit{learning}. Additionally, their ability to \textit{adapt} to changes in
+the actual plant's behaviour should be further addressed.
+
+\section*{Acknowledgements}
+
+I would like to thank Manuel Koch for the great help provided during the course
+of the project starting from the basics on CARNOT modelling, to helping me
+better compare the performance of different controllers, as well as Prof.\ Colin
+Jones, whose insights were always very guiding, while still allowing me to
+discover everything on my own.
+
+\clearpage