Indirect Adaptive MPC for Discrete-Time LTI Systems With Parametric Uncertainties
Abhishek Dhar, Shubhendu Bhasin
Abstract
This article addresses the problem of controlling discrete-time linear time-invariant systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed gradient-descent-based indirect adaptive controller, used to handle parametric uncertainties, is combined with a model predictive control (MPC) algorithm, which guarantees constraint satisfaction. An estimated model of the actual 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 the model mismatch between the estimated plant 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 and the closed-loop system is proved to be bounded at all instants and asymptotically converging to the origin.