Lagrange-Based Global Self-Optimizing Control for Constraint Activeness Varying Processes

Self-optimizing control (SOC) aiming to select most appropriate controlled variables (CVs), is a promising control strategy in the field of real-time optimization. An approach, global self-optimizing control (gSOC) was proposed to find globally optimal CVs by minimizing the global average of the economic loss over the whole operation space. However, as the gSOC was developed from the local SOC, it inherited the same theoretical basis by assuming invariant constraint activeness. Nevertheless, this will significantly restrict the applicable range of SOC as in many real systems activeness varying constraints are common. The difficulty for the gSOC to consider activeness varying constraints is the degrees of freedom inconsistency in CV selection. To tackle the problem, this paper rebuilds the gSOC approach based on the Lagrange function and the well known Karush-Kuhn-Tucker conditions to incorporate active and inactive constraints uniformly in a Lagrange-based global average loss expression. As the gSOC approach is based on optimal measurement data, optimal values of the newly introduced Lagrange multiplies can also be obtained from the same optimization results as well. With this novel Lagrange-based loss function, an optimization problem for CV selection is formulated although non-convex. Thus, the short-cut algorithm of the original gSOC approach is amended for the Lagrange-based gSOC (LgSOC) problem to derive a closed-form solution. Furthermore, the existing cascade SOC structure for a single constraint is generalized to guarantee all constraints satisfied in the whole space. The proposed LgSOC method was proved effective to solve constraint activeness varying gSOC problems through an evaporator case study.