Bias Correction of Discounted Optimal Steady-State using Cost Modification

In the literature of Economic Model Predictive Control (EMPC) and undiscounted Optimal Control Problem (OCP), the optimal steady-state point is an equilibrium point with the minimum stage cost. If the Economic MPC is discounted, this property does not hold, and the optimal steady-state point is not the same as the one obtained from the undiscounted EMPC. Therefore the discounted steady-state point does not yield minimum stage cost and has a bias with respect to the undiscounted one. In this paper, we propose a computationally inexpensive cost modification in the discounted MPC that results in the undiscounted optimal steady-state point, i.e., the steady-state point that leads to the best stage cost. Moreover, we show that this modification does not affect the closed-loop system behavior. We illustrate the proposed method in a numerical example.