Adaptive Robust Output Feedback MPC of Constrained Linear Systems using Guaranteed Parameter Estimation^*

Robust MPC schemes address the presence of uncertainties in the model to achieve robust constraint satisfaction and stability of the closed-loop. A significant improvement of the performance of robust MPC schemes is possible by utilizing real-time measurement data from the controlled system to adapt the model uncertainty that is used in the controller online. We consider a linear system that is affected by both additive and multiplicative uncertainties. The true parametric uncertainty of the system is assumed to be contained in a convex polytopic set and time-invariant. In addition, it is considered that not all states are measured and that the measurements are affected by noise. We propose an adaptive robust MPC scheme that can handle uncertainties and can systematically update the limits of the unknown parameters in the system at every time step. The unknown but constant parameters are estimated using guaranteed parameter estimation. Recursive feasibility and robust stabilizing capabilities of the proposed approach are proven. Two examples are presented to show the benefits of the proposed adaptive scheme.