Multi-Model Indirect Adaptive MPC

This paper addresses the regulation problem of discrete-time linear time-invariant (LTI) systems with parametric uncertainties in the presence of hard state and input constraints. An indirect adaptive identifier is strategically fused with MPC to ensure constraint satisfaction in presence of parametric uncertainties. The estimated plant model, based on indirect adaptive identifier, is used for future state prediction in the MPC algorithm. An estimated model of the actual uncertain plant is used for predictions of the future states. The estimated plant parameters belong to a convex model set, whose vertices are updated using a gradient descent based adaptive update law, the convex combination of which yields the plant parameter estimates. The errors arising due to model mismatch between the estimated plant model and the actual uncertain plant are accounted for in the MPC algorithm, using a constraint tightening method, which is dependent upon the diameter of the model set. Therefore, the magnitude of constraint tightening is reduced whenever better knowledge of the updated model set is obtained. The proposed adaptive MPC strategy is proved to be recursively feasible and the closed-loop system states are proved to be bounded and asymptotically converging to the origin.