Constrained output regulation for linear systems performing iterative tasks via robust learning MPC

The constrained output regulation problem has been addressed by the output feedback model predictive control (MPC) algorithm for deterministic system without random disturbances in recent years. This paper further considers the case with the presence of unknown-but-bounded random disturbances in the linear systems performing iterative regulation tasks, which have not been considered. When pursuing infinite-horizon optimization, unknown random disturbances give rise to an infinite horizon policy optimization problem in the MPC controller, and the problem cannot be directly solved. Moreover, the recursive feasibility in dealing with iterative tasks for the deterministic system cannot be guaranteed for uncertain systems, which renders the solution of this paper nontrivial. To this end, we develop a novel robust learning-based MPC algorithm such that the problem of linear iterative output regulation in the presence of unknown-but-bounded random disturbances along with state and input constraints is addressed.