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Model predictive control is a very successful modern control technology, which consists of repeatedly solving a finite horizon optimal control problem and then applying the first part of the solution to the considered system. The main advantages of MPC and the reasons for its widespread success are that (i) satisfaction of input and state constraints for the closed-loop system can be guaranteed, (ii) optimization of some performance criterion is directly incorporated in the controller design, and (iii) it can be applied to (possibly nonlinear) systems with multiple inputs. In many applications, only an uncertain model of the underlying system is available, or a suitable parametric model might be difficult or very expensive to obtain. In these cases, MPC approaches which allow for an online adaptation or learning of the underlying model are of crucial importance. While significant progress has been made in recent years in the context of robust MPC, where disturbance/uncertainty bounds are assumed to be fixed and given a priori, much less results have been obtained in the context of adaptive and learning-based MPC, where many important question are still unanswered. Not least because of the tremendous success of machine learning in many application areas, the question of how to beneficially employ learning techniques in the context of systems and control has received an increasing amount of attention in recent years. The purpose of this special issue is to present a collection of recent advances in this exciting and highly topical research area by renowned research groups worldwide. The scope of the special issue includes robust and stochastic MPC approaches with online parameter/uncertainty adaptation, learningand data-based MPC techniques, as well as applications thereof in different areas. In particular, the following contributions are included in this special issue: In their paper Indirect adaptive model predictive control and its application to uncertain linear systems, Di Cairano and Danielson propose an adaptive MPC scheme for general nonlinear systems subject to unknown parameters that are constant or slowly time-varying and establish closed-loop constraint satisfaction and input-to-state stability with respect to the parameter estimation error. For the special case of linear systems with parametric uncertainty, it is shown how the proposed scheme can efficiently be implemented. Lu, Cannon and Koksal-Roivet study linear systems with parametric uncertainty and additive disturbances in their contribution Robust adaptive model predictive control: Performance and parameter estimation. Robust constraint satisfaction and input-to-state stability are shown for the proposed adaptive MPC approach, while computational tractability is ensured using polytopic sets of fixed complexity for the parameter estimates and predicted trajectories. Furthermore, a convex constraint is proposed to ensure persistence of excitation, which can be used to prove (probabilistic) convergence of the estimated parameter set to the true unknown parameter value. The paper A robust adaptive model predictive control framework for nonlinear uncertain systems by Köhler, Kötting, Soloperto, Allgöwer and Müller proposes a computationally efficient adaptive MPC framework for nonlinear systems with an affine dependence on unknown parameters and subject to additive disturbances. Set membership estimation is employed to ensure robust constraint satisfaction, while an additional point estimate of the unknown parameters is used to ensure finite-gain 2-stability with respect to the additive disturbances. In their paper Robust Adaptive Model Predictive Control for Guaranteed Fast and Accurate Stabilization in the Presence of Model Errors, Pereida, Brunke and Schoellig propose a robust adaptive model predictive controller termed RMPC-1 controller. The proposed approach combines robust model predictive control with an underlying discrete-time1 adaptive controller for which the authors prove closed-loop stability and recursive feasibility. The paper Online learning-based Model Predictive Control with Gaussian Process Models and Stability Guarantees by Maiworm, Limon and Findeisen employs evolving Gaussian Processes to define and online adapt a system model. Under suitable conditions on the data sets used for online model updates, closed-loop constraint satisfaction and input-to-state stability with respect to the model error is established. Kinky inference methods are employed by Manzano, Muñoz de la Peña, Calliess and Limon in their contribution Online learning constrained model predictive control based on double prediction. In particular, two different models are used, one that is determined offline to ensure robust constraint satisfaction (safety), and one that is updated online to