Reduced SARX modeling and control via Regression Trees

In this work a complexity reduction methodology is proposed for a data-driven Switched Auto-Regressive eXogenous (SARX) model identification algorithm based on Regression Trees. In particular, we aim at reducing the number of submodels of a SARX dynamical model without compromising (and indeed improving) the model accuracy, and mitigating the overfitting problem. A validation procedure is addressed to compare the performance of the reduced model with respect to the original one. Results show an important reduction in the number of modes of the identified model that ranges between 96% and 99.74%. The accuracy of the reduced model is also tested in terms of closed-loop control performance in a Model Predictive Control (MPC) setup, on a benchmark consisting of a non-linear inverted pendulum on a cart: the comparison is provided with respect to an oracle, i.e. an MPC setup with perfect knowledge of the plant dynamics.