Prediction regions based on dissimilarity functions.

This paper presents a new methodology to obtain prediction regions of the output of a dynamical system. The proposed approach uses stored past outputs of the system and it is entirely data-based. Only two hyperparameters are necessary to apply the proposed methodology. These scalars are chosen so that the size of the obtained regions is minimized while fulfilling the desired empirical probability in a validation set. In this paper, methods to optimally estimate both hyperparameters are provided. The provided prediction regions are convex and checking if a given point belongs to a computed prediction region amounts to solving a convex optimization problem. Also, approximation methods to build ellipsoidal prediction regions are provided. These approximations are useful when explicit descriptions of the regions are necessary. Finally, some numerical examples and comparisons for the case of a non-linear uncertain kite system are provided to prove the effectiveness of the proposed methodology. • A method to compute prediction regions for multivariate systems is presented. • These regions contain future values of the outputs with a certain probability. • The proposed method does not need any knowledge of the system dynamics. • A procedure to obtain ellipsoidal approximations of the regions is also presented. • The results are illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]