Offset-Free Economic MPC Based on Modifier Adaptation: Investigation of Several Gradient-Estimation Techniques

Abstract

Various offset-free economic model predictive control schemes that include a disturbance model and the modifier-adaptation principle have been proposed in recent years. These schemes are able to reach plant optimality asymptotically even in the presence of plant–model mismatch. All schemes are affected by a major issue that is common to all modifier-adaptation formulations, namely, plant optimality (note that convergence per se does not require perfect plant gradients) requires perfect knowledge of static plant gradients, which is a piece of information not known in most practical applications. To address this issue, we present two gradient-estimation techniques, one based on Broyden’s update and the other one on linear regression. We apply these techniques for the estimation of either the plant gradients or the modifiers directly. The resulting economic MPC schemes are tested in a simulation and compared on two benchmark examples of different complexity with respect to both convergence speed and robustness to measurement noise.

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

“…This does not ensure convergence to an optimal steady state (21) in case of an economic stage cost ℓ e . Modifier adaptation estimates a correction for the steady-state optimization (21) that ensures convergence to the (economically) optimal steady state (Alamo et al, 2014;Faulwasser and Pannocchia, 2019;Vaccari et al, 2021). Developing similar approaches for more dynamic problems (C.1) is an open problem.…”

Economic MPC with Modifier Adaptation using Transient Measurements

“…DME uses an optimization algorithm executed on-line to make the estimated modifiers converge to the ones in steady state required by MA. More recently, Vaccari et al (2021) presented a extension of Vaccari et al (2020) to compare two techniques to estimate either plant gradients or modifiers using steady-state measurements via Broyden's update and linear regression. The eMPC schemes were tested in simulation in two benchmark examples, stressing the fact that the use of transient measurements to estimate the process gradients can be an interesting approach to speed up convergence.…”