Economic Nonlinear MPC for Conflicting Control Objectives with Constructive Stability Guarantees: A Two-Fold Application Case Study

Economic Nonlinear Model Predictive Control (E-NMPC) is a peculiar variant of classic NMPC, which directly includes an economic criterion within its stage cost function, allowing to steer the system under control towards an economically optimal equilibrium and ensuring a profitable economic performance during the transient. While its formulation provides significant advantages for many practical applications, E-NMPC suffers from two main drawbacks: first, it only accounts for the economic objective, disregarding additional conflicting tasks, such as tracking; second, it forfeits classical Lyapunov-based stability guarantees, since, in general, its stage cost is non-minimal at the optimal economic equilibrium. To address these limitations, we present a novel E-NMPC formulation, accounting for both economic and tracking tasks together. Additionally, we propose a general constructive procedure to design suitable stabilizing terms for E-NMPC, ensuring its closed-loop stability with minimal impact on the economic performance. Our E-NMPC approach is validated on two different case studies: energy-efficient Adaptive Cruise Control (ACC) in electric vehicles, and mitigation of epidemic spreading on networks via vaccination and non-pharmaceutical interventions (NPIs).