Experimental gradient estimation of multivariable systems with correlation by various regression methods and its application to modifier adaptation

Abstract In process optimization, model-plant mismatch is an important issue because it is closely related to the economic competitiveness of the product. To handle this issue, experimental gradient-based methods, such as modifier adaptation scheme, that ensure the necessary conditions of optimality for the plant equations have been utilized. However, gradient estimation methods may not work properly for the conventional modifier adaptation scheme in the case of multivariable systems with correlation. In this paper, we compare the optimization performance of gradient estimation for conventional modifier adaptation approaches and regression methods, such as multivariable linear regression, partial least squares regression, and principal component analysis. The moving average input update strategy and latent variable space model based algorithm are proposed to suppress excessive updates and improve the convergence rate and stability near the Karush-Kuhn-Tucker (KKT) point. Several simulation results of fed-batch operation of a bioreactor show that regression-based methods, especially latent variable space modelling, outperform conventional methods in the optimization of the multivariable system with correlation. In addition, the simulations show that both fast convergence and stability near the KKT point can be achieved by using the proposed latent variable space model-based algorithm.