Enhanced global self-optimizing control

Global self-optimizing control (gSOC) is a recent development in selecting controlled variables (CVs) to ensure the resulting control system can achieve satisfactory self optimizing performance in the entire operation range. In Ye et al (2015), the gSOC problem was solved by using data collected under the necessary condition of optimality (NCO). In particular, a short-cut algorithm was proposed to solve the problem efficiently. The short-cut gSOC algorithm assumes the Hessian of the cost function against CVs is constant in the entire operation space so that the loss expression can be significantly simplified. Certainly, this assumption is not generally true. To compensate this deficiency. a constraint of the Hessian is enforced at a reference point. However, how to determine the reference point and whether the selection of reference point will affect the optimality of CVs selected are not answered. Focusing on this deficiency, this paper proposed a Ile W algorithm to enhance the gSOC solution. Firstly, the constraint at a reference point is relaxed to be a least squares fitting equation for all data points. This fitting equation is combined with the average loss to form an integrated least squares fitting problem with a weighting coefficient for optimization. The analytical solution to the new problem leads to an enhanced gSOC algorithm. Numerical case studies show that this algorithm can result in CVs very close to theoretically optimal ones.