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Lucas Ferreira Bernardino, Sigurd Skogestad, ''Optimal measurement-based cost gradient estimate for feedback real-time optimization,'' , Computers and Chemical Engineering, vol. 189 (2024), 108815.

The method is very easy. It's just the exact local method of self-optimization control (Alstad, Skogestad, Hhori, 2009), but with the right choice of directions (which is a degree of freedom in self-optimizing control because there we have an additional feedback controller). The nice things is that all the calculations to find H are offline and done only once. Online it’s a data-based method which simply is a combination of the measurements, Ju = H y.