${\widehat{A}}$ to obtain control locations ${\mathcal{D}}$, compute kernel matrix ${{\ensuremath{K}}_{{C}{D}}}\in{\mathbb{R}}^{{\ell}\times{M}}$ between ${\mathcal{D}}$ and ${\mathcal{C}}$, and initialize controller (e.g. LQR) utilizing $({\widehat{A}}, {\widehat{B}})$. 1) Sample data $\{y^i_k\}_{i=1}^{{N}}$ from $f(x,k)$. 2) Utilize observer to estimate ${\widehat{w}}_{k+1}$. 3) Use ${\widehat{w}}_{k+1}$ and $f_{\text{ref}}$ as input to controller to get feedback.

Experimental Results {#sec:experimental_results}
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We report experimental results on controlling synthetic and modeling real-world data. All experiments were performed using MATLAB on a laptop running Ubuntu 14.04 with $8$ GB of RAM, and an Intel core i7 processor.

Prediction of global ocean surface temperature
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We first analyzed the feasibility of this modeling approach on a large dataset: the $4$ km AVHRR Pathfinder project, which is a satellite monitoring global ocean surface temperature. This data was obtained from the National Oceanographic Data Center. The data consists of longitude-latitude measurements on a 2D domain ${\Omega}\subset[-180,180]\times[-90,90]$; this dataset is challenging, with measurements at over $37$ million coordinates, and several missing pieces of data. The goal was to learn the day and night temperature models $f_k(x,y)\in{\ensuremath{{\mathcal{H}}_{{C}}}}$, where ${\ensuremath{{\mathcal{H}}_{{C}}}}$ was generated using the Gaussian kernel ${k}(x,y) = e^{-(\|x-y\|^2/2{\sigma}^2)}$. We first did a search for the ideal bandwidth ${\sigma}$ for a $304$-dimensional sparse Gaussian process model with a Gaussian 