(542h) Partial Multiparametric Programming for Accelerating Optimal Control, Applied to an Air Separation Unit

Multiparametric programming is the mathematical optimization methodology of solving optimization problems explicitly and offline with applications to optimal control[1], simultaneous design and control[2], and multilevel optimization[3]. However, as the optimization problem size grows in size, generating the full explicit solution becomes increasingly burdensome to calculate and store. To address these issues, we propose an approach where the online optimization problem is augmented with information derived from the multiparametric programming problem.

This presentation describes a novel multiparametric programming-based approach to reducing the number of constraints that must be considered in the online step by generating bounds in the parametric space where the constraints appear in an optimal basis. These bounds are generated via a bilevel optimization approach reformulated as a single-level optimization problem based on substituting the KKT conditions. After these bounds are calculated, they can be utilized in the online setting to remove any constraints that do not need to be considered. Due to the nature of the bounds, the memory requirement to store the bounds is low. This procedure can be viewed as an aggressive dynamic pre-solving procedure where some optimality aspects are known ahead of time.

The proposed procedure is then on an optimization-based control case study of an Air Separation Unit (ASU). Where the optimization problem to solve repeatedly is the optimal control problem introduced by a Model Predictive Controller (MPC). This MPC is then recast as a multiparametric MPC. The constraint bounds procedure is then applied. With this, the bounds of applicability are known for every constraint as a function of the process state. We will show that this procedure reduces the computational load of resolving the proceeding optimization problems at each step. This general procedure applies to other applications where optimization problems must be resolved frequently.

[1] - I. Pappas, D. Kenefake, B. Burnak, S. Avraamidou, H. S. Ganesh, J. Katz, N. A. Diangelakis, E. N. Pistikopoulos, 2021. Multiparametric programming in process systems engineering: Recent developments and path forward. Frontiers in Chemical Engineering 2, 32.

[2] - B. Burnak, N. A. Diangelakis, J. Katz, E. N. Pistikopoulos, 2019. Integrated process design, scheduling, and control using multiparametric programming. Computers & Chemical Engineering 125, 164–184

[3] - S. Avraamidou, E. N. Pistikopoulos, 2019. B-pop: Bi-level parametric optimization toolbox. Computers & Chemical Engineering 122, 193 – 202, 2017 Edition of the European Symposium on Computer Aided Process Engineering (ESCAPE-27)