This dissertation presents contributions mainly in three different fields: system
identification, probabilistic forecasting and stochastic control.
Thanks to the concept of dissimilarity and by defining an appropriate dissimilarity
function, it is shown that a family of predictors can be obtained. First, a
predictor to compute nominal forecastings of a time-series or a dynamical system
is presented. The effectiveness of the predictor is shown by means of a numerical
example, where daily predictions of a stock index are computed. The obtained
results turn out to be better than those obtained with popular machine learning
techniques like Neural Networks.
Similarly, the aforementioned dissimilarity function can be used to compute conditioned
probability distributions. By means of the obtained distributions, interval
predictions can be made by using the concept of quantiles. However, in order to
do that, it is necessary to integrate the distribution for all the possible values of
the output. As this numerical integration process is computationally expensive,
an alternate method bypassing the computation of the probability distribution is
also proposed. Not only is computationally cheaper but it also allows to compute
prediction regions, which are the multivariate version of the interval predictions.
Both methods present better results than other baseline approaches in a set of
examples, including a stock forecasting example and the prediction of the Lorenz
attractor.
Furthermore, new methods to obtain models of nonlinear systems by means of
input-output data are proposed. Two different model approaches are presented:
a local data approach and a kernel-based approach. A kalman filter can be added
to improve the quality of the predictions. It is shown that the forecasting performance
of the proposed models is better than other machine learning methods in
several examples, such as the forecasting of the sunspot number and the R¨ossler
attractor. Also, as these models are suitable for Model Predictive Control (MPC),
new MPC formulations are proposed. Thanks to the distinctive features of the
proposed models, the nonlinear MPC problem can be posed as a simple quadratic
programming problem. Finally, by means of a simulation example and a real
experiment, it is shown that the controller performs adequately.
On the other hand, in the field of stochastic control, several methods to bound
the constraint violation rate of any controller under the presence of bounded or
unbounded disturbances are presented. These can be used, for example, to tune
some hyperparameters of the controller. Some simulation examples are proposed
in order to show the functioning of the algorithms. One of these examples considers
the management of a data center. Here, an energy-efficient MPC-inspired policy is developed in order to reduce the electricity consumption while keeping
the quality of service at acceptable levels
