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Fixed unconsistent use of acronyms

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Radu C. Martin 2021-07-22 22:13:51 +02:00
parent 1e1cc5acd8
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7 changed files with 49 additions and 47 deletions
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18
Sections/70_Implementation.tex
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@ -48,7 +48,7 @@ the correct amount of data for the weather predictions and to properly generate
the optimization problem, the discrete/continuous transition and vice-versa
happens on the Simulink side. This simplifies the adjustment of the sampling
time, with the downside of harder inclusion of meta-data such as hour of the
day, day of the week, etc.\ in the \acrlong{gp} Model.
day, day of the week, etc.\ in the \acrshort{gp} Model.
The weather prediction is done using the information present in the CARNOT
\acrshort{wdb} object. Since the sampling time and control horizon of the
@ -66,13 +66,13 @@ evaluating a \acrshort{gp} has an algorithmic complexity of $\mathcal{O}(n^3)$.
This means that naive implementations can get too expensive in terms of
computation time very quickly.
In order to have as smallest of a bottleneck as possible when dealing with
\acrshort{gp}s, a very fast implementation of \acrlong{gp} Models was used, in
the form of GPflow~\cite{matthewsGPflowGaussianProcess2017}. It is based on
TensorFlow~\cite{tensorflow2015-whitepaper}, which has very efficient
implementation of all the necessary Linear Algebra operations. Another benefit
of this implementation is the very simple use of any additional computational
resources, such as a GPU, TPU, etc.
In order to have as smallest of a bottleneck as possible when dealing with the
required algebraic operations, a very fast implementation of \acrshort{gp}
Models was used, in the form of GPflow~\cite{matthewsGPflowGaussianProcess2017}.
It is based on TensorFlow~\cite{tensorflow2015-whitepaper}, which has very
efficient implementation of all the necessary Linear Algebra operations. Another
benefit of this implementation is the very simple use of any additional
computational resources, such as a GPU, TPU, etc.
\subsubsection{Classical Gaussian Process training}
@ -158,7 +158,7 @@ Let $w_l$, $u_l$, and $y_l$ be the lengths of the state vector components
$\mathbf{w}$, $\mathbf{u}$, $\mathbf{y}$ (cf. Equation~\ref{eq:components}).
Also, let X be the matrix of all the system states over the optimization horizon
and W be the matrix of the predicted disturbances for all the future steps. The
original \acrlong{ocp} can be rewritten using index notation as:
original \acrshort{ocp} can be rewritten using index notation as:
\begin{subequations}\label{eq:sparse_optimal_control_problem}
\begin{align}