Adaptive Economic Model Predictive Control: Performance Guarantees for Nonlinear Systems

TL;DR

This paper introduces an adaptive economic MPC framework for nonlinear systems that optimizes transient economic costs, handles uncertainties via online adaptation, and guarantees robustness and performance bounds.

Contribution

It presents a novel adaptive economic MPC method combining online model adaptation, optimal setpoint determination, and robust tube-based control for nonlinear systems.

Findings

Ensures recursive feasibility and constraint satisfaction.

Provides a performance bound relative to the best steady-state operation.

Demonstrates effectiveness in a chemical reactor example.

Abstract

We consider the problem of optimizing the economic performance of nonlinear constrained systems subject to uncertain time-varying parameters and bounded disturbances. In particular, we propose an adaptive economic model predictive control (MPC) framework that: (i) directly minimizes transient economic costs, (ii) addresses parametric uncertainty through online model adaptation, (iii) determines optimal setpoints online, and (iv) ensures robustness by using a tube-based approach. The proposed design ensures recursive feasibility, robust constraint satisfaction, and a transient performance bound. In case the disturbances have a finite energy and the parameter variations have a finite path length, the asymptotic average performance is (approximately) not worse than the performance obtained when operating at the best reachable steady-state. We highlight performance benefits in a numerical example involving a chemical reactor with unknown time-invariant and time-varying parameters.