Enhancing Output-Feedback MPC With Set-Valued Moving Horizon Estimation

We consider output feedback control of linear discrete-time systems subject to bounded additive disturbances and measurement noise. The goal is to stabilize the system while ensuring the satisfaction of hard constraints on the state and input. For this purpose, we present a novel output-feedback model predictive control (MPC) scheme based on set-valued estimation. The main feature of the scheme is that the number of past measurements used in order to obtain the set-valued estimate depends on the particular time step in the prediction horizon for which the estimate is required. In particular, we employ fewer measurements for prediction steps that are farther in the future, which is a key point in establishing recursive feasibility. The resulting optimal control problem is of bounded complexity, which is a priori known, and is a linearly constrained convex optimization problem under additional assumptions. We demonstrate in a numerical example that the proposed MPC scheme allows an enlargement of the feasible set beyond what is possible with earlier schemes using only linear estimators.