Model learning from data: from centralized multi-model regression to distributed cloud-aided single-model estimation

This thesis presents a collection of methods for learning models from data, looking at this problem from two perspectives: learning multiple models from a single data source and how to switch among them, and learning a single model from data collected from multiple sources. Regarding the first, to describe complex phenomena with simple but yet complete models, we propose a computationally efficient method for Piecewise Affine (PWA) regression. This approach relies on the combined use (i) multi-model Recursive Least-Squares (RLS) and (ii) piecewise linear multi- category discrimination, and shows good performances when used for the identification of Piecewise Affine dynamical systems with eXogenous inputs (PWARX) and Linear Parameter Varying (LPV) models. The technique for PWA regression is then extended to handle the problem of black-box identification of Discrete Hybrid Automata (DHA) from input/output observations, with hidden operating modes. The method for DHA identification is based on multi-model RLS and multicategory discrimination and it can approximate both the continuous affine dynamics and the Finite State Machine (FSM) governing the logical dynamics of the DHA. Two more approaches are presented to tackle the problem of learning models that jump over time. While the technique designed to learn Rarely Jump Models (RJMs) from data relies on the combined solution of a convex optimization problem and the use of Dynamic Programming, the method proposed for Markov Jump Models (MJMs) learning is based on the joint use of clustering plus multi-model RLS and a probabilistic clustering technique. The results of the tests performed on the method for RJMs learning have motivated the design of two techniques for Non-Intrusive Load Monitoring, i.e., to estimate the power consumed by the appliances in an household from aggregated measurements, which are also presented in the thesis. In particular, methods based on (i) the optimization of a least-square error cost function, modified to account for the changes in the appliances operating regime, and relying on (ii) multi-model Kalman filters are proposed. Regarding the second perspective, we propose methods for cloud-aided consensus-based parameter estimation over a multitude of similar devices (such as a mass production). In particular, we focus on the design of RLS-based estimators, which allow to handle (i) linear and (ii) nonlinear consensus constraints and (iii) multi-class estimation