Model Tree Ensembles for Modeling Dynamic Systems

Abstract

We address the task of discrete-time modeling of nonlinear dynamic systems using measured data. In the area of control engineering, this task is typically converted into a classical regression problem, which can then be solved with any nonlinear regression approach. As tree ensembles are a very successful predictive modelling approach, we investigate the use of tree ensembles for regression for this task.

While ensembles of regression trees have been extensively used and different variants thereof explored (such as bagging and random forests), ensembles of model trees have received much less attention, being limited mostly to bagging of model trees. We introduce a novel model tree ensemble approach to regression, namely, bagging and random forests of fuzzified model trees. The main advantage of the new approach is that it produces a model with no discontinuities with a satisfactory extrapolation behavior, needed for modeling dynamic systems.

We evaluate existing tree ensemble approaches to regression and the approach we propose on two synthetic and one real task of modeling nonlinear dynamic systems coming from the area of control engineering. The results show that our proposed model tree ensembles outperform ensembles of regression trees and have comparable performance to state-of-the-art methods for system identification typically used in control engineering. The computing time of our approach is comparable to that of the state-of-the-art methods on the small problems considered, with the potential to scale much better to large modeling problems.