Indirect Adaptive MPC for Discrete-time LTI system with Robust Constraint Satisfaction

This paper addresses the problem of controlling discrete-time linear time-invariant (LTI) systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed indirect adaptive controller is combined with a model predictive control (MPC) algorithm. An estimated model, corresponding to the uncertain plant, is used for predictions of the future states. The parameters of the estimated model are updated using a gradient descent based adaptive update law. The errors arising due to model mismatch between the estimated system model and the actual uncertain plant are accounted for using a constraint tightening method in the MPC algorithm. The proposed adaptive MPC strategy is proved to be recursively feasible.