# Gaussian Processes for Signal Processing and Representation in Control Engineering
###### Abstract  
The Gaussian process is an increasingly well-known type of stochastic process, which is a generalization of the Gaussian probability distribution. It allows us to model complex functions thanks to its flexibility, which would not be possible with the use of other tools. Gaussian processes also have a couple of other features that are used in various branches of automation with positive results, ranging from industrial processes to image processing. There are also many ways of setting up the Gaussian processes, which required knowledge on the topic and depend on the presented problem. Considerations on these topics lead to the conclusion that the current state of practical usefulness of Gaussian processes increases significantly, therefore the deepening of knowledge about the ways of its use is highly suggested. In this review, we present selected technical applications of Gaussian Processes allowing an understanding of their broad applicability.  
Gaussian process; control engineering; signal processing; practical applications; optimization; modelling +
Footnote †: journal: _Sci  
* machine learning applications for speech recognition, like [2];
* finance risk management [3];
* structural chemistry [4].  
There are also works, covering technical (computational) aspects of GPs, like [5].  
In our review we focus on applications of GPs in control engineering, discuss relevant issues connected and propose of future directions in this field. Introduction of GPs in control engineering is a relatively recent development. The reason for it were computational issues with large matrix inversions [6]. Modern computing power, efficient algorithms and accessible software allow fitting GPs to a wide scope of problems provided data are available. Applications of GPs.  
Applications of GPs are many, but we can group them into problems such as regression, classification, prediction etc. Regardless of the problem, a well-chosen and set up GP can handle with numerous cases. Its appropriate application to problems where it outclasses the competition is the key. The most common of such cases are problems where obtaining data is difficult or they are deficient, and when problems are difficult to model using other methods [7,8].  
Of course, it is not possible to cover all the currently usage on each issue equally, so we would like to describe as widely as possible the field of the use of GP. Our goal is to reliably determine the current state of the field and draw conclusions from it. We connect specific examples of problems with industrial branches, problems where modeling is difficult, decision control support, where the time of the operation is important, and many more. However, besides the solutions themselves, it is also worth considering the essence of a way of accomplishing them with a range of possibility of methods of handling the problems which occur with its usage. We organised the rest of the paper in the following way. First, we present a basic theory of GPs. Then we show computational methods and problems correlated to them. The next few sections introduce various examples of GP usage in practice in broadly understood control engineering. Paper ends with discussion, proposed future direction and conclusions.