Towards automated data-driven modeling of linear parameter-varying systems

The Linear Parameter-Varying (LPV) paradigm represents a natural extension of the classical Linear Time-Invariant (LTI) framework. By virtue of the so-called scheduling signal, LPV models can accurately describe the behavior of a large class of timevarying and nonlinear dynamical systems, while preserving the linearity between input and output signals. Thus, LPV models are of great practical significance for modeling and control of many industrial systems, as the simplicity of the LTI theory is retained. This thesis is concerned with datadriven modeling of LPV systems, addressing some of the well-known issues pertaining to LPV model identification. In particular, the main research questions addressed in this contribution include selection of the model structure, dealing with noisy measurements of the scheduling signal, identification of the plant model from closed-loop data, and identification of linear fractional representations of LPV models which are especially suitable for controller synthesis. The proposed methodologies mainly fall under the framework of parametric and non-parametric LPV identification using machine learning techniques and provide a set of tools for automated selection of LPV modeling parameters. Furthermore, as an alternative to the conventional parametric and nonparametric approaches, a novel algorithm based on mixedinteger programming is devised for identifying LPV models through piecewise affine regression. The framework of this algorithm is applied to the problem of energy disaggregation with a real-world benchmark dataset.