Homothetic Tube-Based Adaptive MPC

This article presents a homothetic tube-based adaptive model predictive control strategy to handle discrete-time linear time-invariant (LTI) systems with parametric uncertainties and hard constraints imposed on the states and the control inputs. The proposed solution systematically fuses a gradient descent-based adaptive parameter identification strategy with a suitably designed tube-based model predictive controller (MPC). An estimated model is utilized in the MPC for the purpose of state predictions. The parameters of the estimated plant model are updated at every time instant through an adaptive update law by utilizing the measured states and inputs from the uncertain plant. The task of satisfying the hard constraints in the presence of errors in state predictions, arising due to model mismatch between the estimated model and the uncertain plant, is accounted for by suitably tightening the constraints within the MPC optimization routine. The proposed tube-based adaptive MPC is analytically proved to be recursively feasible if initially feasible, and the closed-loop states are guaranteed to be bounded and asymptotically converging to the origin. The claimed properties are further validated through a simulation example.