  We propose a novel adaptive learning-based model predictive control (MPC)
scheme for interconnected systems which can be decomposed into several smaller
dynamically coupled subsystems with uncertain coupling. The proposed scheme is
mainly divided into two main online phases; a learning phase and an adaptation
phase. Set membership identification is used in the learning phase to learn an
uncertainty set that contains the coupling strength using online data. In the
adaptation phase, rigid tube-based robust MPC is used to compute the optimal
predicted states and inputs. Besides computing the optimal trajectories, the
MPC ingredients are adapted in the adaptation phase taking the learnt
uncertainty set into account. These MPC ingredients include the prestabilizing
controller, the rigid tube, the tightened constraints and the terminal
ingredients. The recursive feasibility of the proposed scheme as well as the
stability of the corresponding closed-loop system are discussed. The developed
scheme is compared in simulations to existing schemes including robust,
adaptive and learning-based MPC.
