Min-max constrained infinite horizon model predictive control: Standard vs. feedback formulation

Two robust model predictive controllers based on input/output models and an infinite prediction horizon are formulated and compared. The infinite horizon Generalised Predictive Control (GPC
^∞
), which guarantees the stability of the nominal closed-loop system, is combined with a global uncertainty description and an uncertainty band updating procedure to obtain robust MPC schemes which can be used even when hard non-linearities occur. The suggested control laws involve a min-max optimisation problem which can be solved using common non-linear optimisation tools, such as Sequential Quadratic Programming. The standard min-max approach is compared to the more recent feedback form of the optimisation problem. The latter takes advantage of the notion that feedback is present in the receding-horizon of the controller, and is shown to overcome some of the drawbacks of the former. As a result, an improved performance is obtained, though a somewhat larger computational burden is required.