Methods and applications of distributed and decentralized model predictive control

This thesis deals with the theoretical development of distributed and decentralized control algorithms based on Model Predictive Control (MPC) for linear systems subject to constraints on inputs and states. In all the presented techniques, the basic idea consists in considering the coupling terms among the subsystems as disturbances to be rejected. Part of this disturbance is assumed to be known over all the prediction horizon, while the remaining one is considered unknown but bounded. To reject this second term, a robust approach is implemented using polytopic invariant sets. A regulation problem for distributed control is initially described, together with some practical solutions needed to deal with implementation issues. A continuous-time version of the proposed approach is also provided. Secondly, two different distributed solutions to the tracking problem are given. In the first one, developed for tracking piecewise constant setpoints, a fictitious reference signal is used to guarantee feasibility. The second one, instead, can be used for tracking constant setpoints and relies on the description of the dynamic system in the so-called “velocity-form”, which allows one to insert an integral action in the closed-loop. The properties of systems described in velocity-form are then investigated for the centralized case. Finally, the results derived for the centralized systems in velocity-form are used to develop a completely decentralized approach with integral action for tracking piecewise constant references. Several simulation examples are reported to show the performances of the proposed algorithms.

Questa tesi presenta lo sviluppo teorico di algoritmi di controllo predittivo (Model Predictive Control: MPC) distribuito e decentralizzato. Gli algoritmi permettono di controllare sistemi lineari soggetti a vincoli sugli input e sugli stati. In tutte le tecniche di controllo presentate l'idea comune consiste nel considerare i termini di accoppiamento tra i sottosistemi come disturbi da reiettare. Parte del disturbo è noto su tutto l'orizzonte di previsione, mentre la la parte restante è supposta sconosciuta ma limitata. Per reiettare questo secondo termine è stato impiegato un approccio robusto basato su set invarianti politopici. Inizialmente viene descritta una soluzione distribuita per un problema di regolazione, sia per sistemi discreti che a tempo continuo. In seguito vengono illustrati due differenti approcci distribuiti per la soluzione al problema del tracking. Infine viene enunciato un algoritmo per il tracking decentralizzato.