Regional models and minimal learning machines for nonlinear dynamical system identification

Abstract

This thesis addresses the problem of identifying nonlinear dynamic systems from a machine learning perspective. In this context, very little is assumed to be known about the system under investigation, and the only source of information comes from input/output measurements on the system. It corresponds to the black-box modeling approach. Numerous strategies and models have been proposed over the last decades in the machine learning field and applied to modeling tasks in a straightforward way. Despite of this variety, the methods can be roughly categorized into global and local modeling approaches. Global modeling consists in fitting a single regression model to the available data, using the whole set of input and output observations. On the other side of the spectrum stands the local modeling approach, in which the input space is segmented into several small partitions and a specialized regression model is fit to each partition. The first contribution of the thesis is a novel supervised global learning model, the Minimal Learning Machine (MLM). Learning in MLM consists in building a linear mapping between input and output distance matrices and then estimating the nonlinear response from the geometrical configuration of the output points. Given its general formulation, the Minimal Learning Machine is inherently capable of operating on nonlinear regression problems as well as on multidimensional response spaces. Naturally, its characteristics make the MLM able to tackle the system modeling problem. The second significant contribution of the thesis represents a different modeling paradigm, called Regional Modeling (RM), and it is motivated by the parsimonious principle. Regional models stand between the global and local modeling approaches. The proposal consists of a two-level clustering approach in which we first partition the input space using the Self-Organizing Map (SOM), and then perform clustering over the prototypes of the trained SOM. After that, regression models are built over the clusters of SOM prototypes, or regions in the input space. Even though the proposals of the thesis can be thought as quite general regression or supervised learning models, the performance assessment is carried out in the context of system identification. Comprehensive performance evaluation of the proposed models on synthetic and real-world datasets is carried out and the results compared to those achieved by standard global and local models. The experiments illustrate that the proposed methods achieve accuracies that are comparable to, and even better than, more traditional machine learning methods thus offering a valid alternative to such approaches