Model predictive controller matching: Can MPC enjoy small signal properties of my favorite linear controller?

Model predictive control (MPC) strategies can efficiently deal with constraints on system states, inputs, and outputs. However, in contrast with linear control techniques, closed-loop frequency-domain properties of MPC such as sensitivity and robustness to small perturbations are difficult to enforce a priori. This paper considers the problem of transforming a given linear feedback control design, referred to as “favorite controller”, into a model predictive control one. In this way, the MPC controller inherits all the stability, robustness and frequency properties of the given favorite controller in the region around the equilibrium where the constraints are not active. The added value is that the constructed MPC controller is able to properly handle constraints that may be activated during the transient, and that global stability in the set of feasible initial conditions can be guaranteed.