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

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... 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.