Model on Demand : Algorithms, Analysis and Applications

Sammanfattning: System identification deals with the problem of estimating models of dynamical systems from observed data. In this thesis, we focus on the identification of nonlinear models, and, in particular, on the situation that occurs when a very large amount of data is available.Traditional treatments of the estimation problem in statistics and system identification have mainly focused on global modeling approaches, i.e., the model has been optimized on basis of the entire data set. However, when the number of observations grows very large, this approach becomes less attractive to deal with because of the difficulties in specifying model structure and the complexity of the associated optimization problem. Inspired by ideas from local modeling and database systems technology, we have taken a conceptually different point of view. We assume that all available data are stored in a database, and that models are built “on demand” as the actual need arises. When doing so, the bias/variance trade-off inherent to all modeling is optimized locally by adapting the number of data and their relative weighting. For this concept, the name model-on-demand has been adopted.In this thesis we have adopted a weighted regression approach for the modeling part, where a weight sequence is introduced to localize the estimation problem. Two conceptually different approaches for weight selection are discussed, where the first is based on traditional kernel assumptions and the other relies on an explicit optimization stage. Furthermore, two algorithms corresponding to these approaches are presented and their asymptotic properties are analyzed. It is concluded that the optimization approach might produce more accurate predictions, but that it at the same time is more demanding in terms of computational efforts.Compared to global methods, and advantage with the model-on-demand concept is that the models are optimized locally, which might decrease the modeling error. A potential drawback is the computational complexity, both since we have to search for neighborhoods in a multidimensional regressor space, and since the derived estimators are quite demanding in terms of computational resources.Three important applications for the concept are presented. The first one addresses the problem of nonlinear time-domain identification. A number of nonlinear model structures are evaluated from a model-on-demand perspective and it is concluded that the method isuseful for predicting and simulating nonlinear systems provided sufficiently large datasets are available. It is demonstrated through simulations that the prediction errors are in order of magnitude directly comparable to more established modeling tools such as artificial neural nets and fuzzy identification.The second application addresses the frequency-domain identification problems that occur when estimating spectra of time series or frequency responses of linear systems. We show that the model-on-demand approach provides a very good way of estimating such quantities using automatic, adaptive and frequency-dependent choices of frequency resolution. This gives several advantages over traditional spectral analysis techniques.The third application, which is closely related to the first one, is control of nonlinear processes. Here we utilize the predictive power of the model-on-demand estimator for online optimization of control actions. A particular method, model-free predictive control, is presented, that combines model-on-demand estimation with established model predictive control techniques.