Filter-based Additional Constraints to Relax the Model Adequacy Conditions in Modifier Adaptation

Modifier adaptation (MA) is a real-time optimization (RTO) method with the built-in guarantee to reach the plant optimal operating conditions upon convergence despite disturbances and modeling uncertainties. MA requires a model that (i) is adequate, i.e., the reduced Hessian of the Lagrangian is positive definite at the plant optimum, and (ii) with the same inputs variable as the plant. In this paper, we consider the cases where (i) is not satisfied. The contribution of this article is to propose to merge two steps of the standard MA implementation, i.e., the model-based optimization and the filtering steps by the adding of constraints in the problem formulation. It is shown than the suggested addition of constraints does not require any additional assumption compared to standard MA, and that the resulting model adequacy conditions are less stringent. Indeed, strict convexity is only required for the cost function and therefore, there is no need for the convexification or linearisation of the contraints. The successful application and the advantages of this new method are illustrated by means of a standard benchmark case study for RTO algorithms and a numerical example.