Data-driven Nonlinear Model Predictive Control: Stability, Robustness and Offset-free Tracking

The use of data-driven and learning-based models in model predictive control (MPC) has gained an increasing popularity in recent years thanks to the growing availability of data collected in industrial plants and on the development of powerful deep learning techniques. In this framework, the aim of this thesis is to design nonlinear MPC algorithms with guaranteed stability and robustness properties based on data-driven models of the system under control. A particular attention is devoted to the development of strategies that take into account modeling errors and uncertainties, and that guarantee offset-free tracking. The first part of the thesis explores the design of MPC algorithms for incrementally input-to-state stable (δISS) nonlinear systems modeled by recurrent neural networks (RNN). This class of models can be trained using input-output data, and stability properties of the model can be enforced during the training procedure. Considering different RNN architectures, the thesis develops output-feedback MPC algorithms that ensure closed-loop stability, satisfaction of input and incremental input constraints, robust satisfaction of output constraints in presence of uncertainties and offset-free tracking. Moreover, considering a general δISS system, it is presented how it is possible to guarantee stability considering a positive semi-definite stage cost in the MPC optimization problem (e.g. for output weighting), and how it is possible to enlarge the feasibility region employing an artificial reference. The second part of the thesis considers data-driven models in the Koopman framework, and studies how convergence to the origin can be guaranteed in presence of modeling errors. First, an offset-free MPC algorithm is designed for systems modeled using extended dynamic mode decomposition (EDMD). Then, considering kernel based EDMD models, it is shown how asymptotic stability of MPC without terminal ingredients can be achieved provided that there exist suitable bounds on the modeling error. The last part of the thesis presents the application of MPC to the current control in synchronous reluctance motors, showing performance improvement in presence of model uncertainties compared to the baseline control approaches. All the control algorithms developed in the thesis have been theoretically analyzed, and their validity is assessed in simulation examples.