A tracking MPC formulation that is locally equivalent to economic MPC

• We develop a tuning strategy for tracking MPC such that it locally approximates economic MPC up to first order.
• We prove that the proposed tuning exists whenever economic MPC is stabilizing.
• The theoretical developments valid for linear tracking MPC do not directly extend to nonlinear tracking MPC in the presence of nonlinear inequality constraints. We propose a reformulation of the NMPC problem which tackles this issue.
• We propose a numerical method for computing the tuned tracking cost.
• We illustrate the theoretical developments using an example based on an evaporation process.

The stability proof for economic Model Predictive Control (MPC) is in general difficult to establish. In contrast, tracking MPC has well-established and practically applicable stability guarantees, but can yield poor closed-loop performance in terms of the selected economic criterion. In this paper, we derive a formal procedure to design a tracking MPC scheme so as to locally approximate the behaviour of economic MPC. Given an economic stage cost, the desired tracking stage cost can therefore be computed automatically. Because tracking MPC guarantees stability of the closed-loop system, our procedure succeeds if and only if economic MPC is locally stabilising. This fact can be used to certify whether economic MPC is not stabilising. We illustrate the theoretical developments in a simulated example.