Learning meets control. Data analytics for dynamical systems

Abstract

System identification has always been one of the main research focuses of the control community, since the early steps of the automatic control field. The development of a dynamical system’s models from experimental data is instrumental for understanding the plant under study and designing its model-based control scheme. In the last decade, a cross-fertilization began between the System Identification and the Statistical Learning communities. This led firstly to the introduction of regularization techniques in system identification, and, more recently, to the application of kernel methods to dynamical system learning. This thesis further investigates the roles that learning methods can have in the control science. In the first part, we lay the theoretical foundations of a new kernel-based regularization method for Nonlinear Finite Impulse Response (NFIR) system identification. The method, called Semi-Supervised Identification (SSI), relies on the manifold spanned by the system’s inputs. This manifold is constructed by using not only the measured input/output data, but also inputs data for which there is no corresponding outputs. The effect of this rationale is to impose prior information on the system structure, in the form of local smoothness assumptions. This differs from standard Tikhonov regularization, which imposes a global smoothness behaviour on the learned function. The second part of this work presents practical applications of how statistical learning methods can be used to face control and estimation problems. The case studies span a variety of different applications, from fault detection of electro-mechanical actuators, to clustering methodologies and pure forecasting challanges.