Efficient Learning Control through Zonotopic Set Membership Estimation and Scenario MPC^*

Model Predictive Control (MPC) is widely used in control systems due to its proficiency in managing input and state constraints while optimizing controller performance. Nevertheless, applying MPC to systems with uncertain disturbances and unknown dynamics presents formidable challenges. To handle this issue, we propose a learning scenario-MPC approach. An auto-regressive model with exogenous input is iteratively identified, and its parameters are randomly sampled from an updated zonotopic feasible parameter set. The MPC framework is then implemented using the updated auto-regressive model set as dynamic constraints, with a mean cost function, computed across the predefined set of sampled scenarios. This approach leads to a low complexity adaptive control strategy with probabilistic guarantees on constraint satisfaction. The effectiveness of the proposed method is validated on a vehicle path following problem, with unknown vehicle parameters and varying curvatures, where it is shown that the strategy is able to learn the system dynamics from closed-loop data while properly tracking the target path.