Identification of sparse nonlinear controlled variables for near-optimal operation of chemical processes

For optimal operation of chemical processes, the selection of controlled variables plays an important role. A previous proposal is to approximate the necessary conditions of optimality (NCO) as the controlled variables, such that process optimality is automatically maintained by tracking constant zero setpoints. In this paper, we extend the NCO approximation method by identifying sparse nonlinear controlled variables, motivated by the fact that simplicity is always favoured for practical implementations. To this end, the l1$$ {l}_1 $$-regularization is employed to approximate the NCO, such that the controlled variables are maintained simple, even they are specified as nonlinear functions. The sparse controlled variables are solved using the proximal gradient method, implemented within a tailored Adam algorithm. Two case studies are provided to illustrate the proposed approach.