A Terminal Cost for Economic Model Predictive Control with Local Optimality

In this work, we design a terminal cost for economic model predictive control (EMPC) which preserves local optimality. We first show, based on the strong duality and second order sufficient condition (SOSC) of the steady-state optimization problem, that the optimal operation of the system is locally equivalent to an infinite-horizon LQR controller. The proposed terminal cost is constructed as the value function of the LQR controller plus a linear term characterized by the Lagrange multiplier associated with the steady state constraint. EMPC with the proposed terminal cost is stabilizing with an appropriately chosen control horizon, and preserves the local optimality of the LQR controller. Simulation results of an isothermal CSTR verify our analysis.