Probabilistic data-driven methods for forecasting, identification and control

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

Control predictivo basado en partículas y simulaciones de Montecarlo

El Control Predictivo basado en Modelo es, desde su aparición, una de las estrategias de control avanzado más populares y con mayor relevancia en la industria en la actualidad. Continuamente se publican nuevos resultados y avances, consiguiendo cada vez un mejor rendimiento del controlador o proporcionando garantías que antes no existían. Por esta razón, enfocamos el presente trabajo en el estudio de una posible estrategia de Control Predictivo basado en Métodos de Montecarlo o filtros de partículas, la cual tiene el potencial de hacer frente a diferentes tipos de perturbaciones presentes en los sistemas a controlar. En los algoritmos desarrollados a lo largo del proyecto aparecen los conceptos de partícula y escenario, los cuáles tienen una gran importancia en estas páginas. Cada uno de ellos hace referencia a una característica concreta de los algoritmos y de los problemas a resolver. A modo de resumen: • Las partículas hacen referencia a una solución potencial del problema de optimización. Es decir, se utilizan para resolver un problema matemático con un método alternativo a otros más convencionales como pueden ser los gradenciales. • Los escenarios son una realización hipotética y posible de las perturbaciones durante la operación del sistema. Por tanto, el controlador tiene en cuenta algunos de los escenarios posibles para tomar las decisiones respecto al sistema incierto. Los algoritmos se prueban en distintos sistemas con características diferentes así como a diferentes tipos de perturbación, con el objetivo de evaluar la bondad de estos. En el capítulo 5 se presentan todos los ensayos realizados así como los resultados obtenidos.Universidad de Sevilla. Máster en Ingeniería Industria

Procesamiento masivamente paralelo en control predictivo basado en datos

Durante mucho tiempo, la computación paralela ha estado relegada a supercomputadores de grandes centros de investigación. Sin embargo, con la aparición de la arquitectura CUDA en las tarjetas gráficas de NVIDIA (las cuales no suponían una inversión desorbitada), empezó a estar disponible para un público mucho más amplio. Por otro lado, comprobaremos que la programación con las APIs proporcionadas por el CUDA Toolkit se plantea realmente muy similar a la que estamos acostumbrados a usar habitualmente, permitiéndonos usar diversos lenguajes populares como C o Fortran. La razón por la que planteamos el estudio de estas técnicas encuentra su sentido en el hecho de que existen gran cantidad de problemas que pueden beneficiarse del uso de este tipo de soluciones, más ahora que estamos moviendo continuamente cantidades enormes de información. Dicho esto, el objetivo es explorar las distintas posibilidades actuales para programar en la GPU usando software comercial como Matlab y, una vez hecho esto, implementar algoritmos que usen esta tecnología. En concreto, se resuelven principalmente 2 problemas: • Uso de una base de datos para predecir el estado de un sistema dinámico. • Resolución de un problema de control predictivo multivariable usando una base de datos en lugar de un modelo matemático del sistema. También comentaremos las ventajas e inconvenientes de este tipo de soluciones, haciendo especial hincapié en las mejoras de rendimiento que conseguiremos con respecto a las versiones de los algoritmos anteriores sin paralelizar.Universidad de Sevilla. Grado en Ingeniería de Tecnologías Industriale

Probabilistic interval predictor based on dissimilarity functions

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided

Stock Forecasting Using Local Data

Article number 9306750Stock price forecasting is a relevant and challenging problem that has attracted a lot of interest from engineers and scientists. In this paper we apply two techniques for stock price and price intervals forecasting. Both techniques, derived from previous works by the authors, are based on the use of local data extracted from a database. These data are those that correspond to similar market states to the current one. The first technique uses these local data to compute a price forecast by finding an optimal combination of past states that equals the current state. The price forecast is then obtained by combining the past actual prices associated to the past market states. The second technique can be used to forecast prices but its main use is to forecast price intervals that will contain the real future price with a guaranteed probability. This is accomplished by building a probability distribution for the forecasted price and then setting the intervals by a choice of desired percentiles. Thus, this technique can be used in financial risk management. Both techniques are purely data driven and do not need a theoretical description or model of the price trend being forecasted. The proposed techniques adapt very easily to market changes because they use only the subset of the database that it is closer to the current state. Furthermore, the database can be updated as new data is available. Finally, both approaches are highly parallelizable, thus making possible to manage large data sets. As a case study, the proposed approaches have been applied to the k-step forecasting of the Dow Jones Industrial Average index. The results have been validated in relation with some baseline approaches, such as martingale and neural network predictors and quantile regression for the interval forecasting.Ministerio de Ciencia e Innovación (Esapaña) PID2019-106212RB-C4