Multiparametric Programming in Process Systems Engineering: Recent Developments and Path Forward

Pappas, Iosif; Kenefake, Dustin; Burnak, Baris; Avraamidou, Styliani; Ganesh, Hari S.; Katz, Justin; Diangelakis, Nikolaos A.; Pistikopoulos, Efstratios N.

doi:10.3389/fceng.2020.620168

Cited by 35 publications

(24 citation statements)

References 167 publications

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“…Many common decision-making problems that appear in theory and practice are essentially multiparametric programming problems with the values substituted, such as optimal control, planning, and scheduling, moving horizon estimation, and robust optimal control. [32] Inputs, u Disturbances, d Outputs, y…”

Section: Multiparametric Model Predicative Controlmentioning

confidence: 99%

A smart manufacturing strategy for multiparametric model predictive control in air separation systems

Kenefake

Pappas

Avraamidou

et al. 2022

J Adv Manuf & Process

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Recent trends in digitization and automation of information systems have led to the Industry 4.0 revolution in manufacturing systems. With the emergence of integrated “smart” systems that communicate through the cloud, collecting and manipulating the system data became a key yet, challenging component for developing optimal control strategies for these complex systems. In this work, we propose a strategy to address this problem with the case study on an air separation unit (ASU). Our approach involves developing an ASU's controllers via high‐fidelity modeling, studies in data‐driven reduced‐order models, and providing implementable control policies for the high‐fidelity model. Connecting the high‐fidelity model to a smart manufacturing platform allows integration into other smart manufacturing tools and applications. Since the high‐fidelity model is computationally challenging for online optimization tasks, such as model predictive control, surrogate models are generated that represent the high‐fidelity model's behavior. The derived reduced‐order models are then embedded into a model predictive control formulation for the optimal control of the whole process through multiparametric programming. A multiparametric approach based on solving a small portion of the multiparametric program is proposed to reduce the computational overhead. We then close the loop by deploying the developed controllers on the high‐fidelity model for tuning with prospects of employing them on the real industrial plant.

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Section: Multiparametric Model Predicative Controlmentioning

confidence: 99%

A smart manufacturing strategy for multiparametric model predictive control in air separation systems

Kenefake

Pappas

Avraamidou

et al. 2022

J Adv Manuf & Process

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“…This concept is also known as online via offline optimisation and it is shown in Figure 3. Even though mp-MPC is the niche area of mp-P, designing mp-MPCs of nonlinear systems for set-point tracking is still a computationally strenuous task as one has to design an mp-MPC for each set-point based on the algorithms that exist in the literature to date [40]. Next, we review two mathematical techniques that will enable the development of novel multi set-point explicit controllers though the algorithm we propose in the present work.…”

Section: Multi-parametric Programmingmentioning

confidence: 99%

“…In the context of multi-parametric model predictive control, the state of the system at each sampling point is treated as an uncertain parameter and as a result an mp-P with RHS uncertainty arises [10,37,38,40]. Its solution results in the explicit control law, i.e., the control decisions as explicit functions of the system's initial conditions at a sampling instance along with the related CRs.…”

Section: Multi Set-point Explicit Controller Via Multi-parametric Programmingmentioning

confidence: 99%

Multi Set-Point Explicit Model Predictive Control for Nonlinear Process Systems

2021

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In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions.

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“…Multiparametric programming has also been employed as a useful tool for the development of the Pareto front of multiobjective optimization problems through the generation of explicit expressions of the Pareto front as a function of the objectives. 33 Papalexandri and Dimkou 34 proposed one of the first notable contributions to address multiobjective convex mixed-integer nonlinear optimization problems through multiparametric programming. The authors developed an iterative algorithm to construct an approximate Pareto front for simultaneous process synthesis/planning and product/process design problems under uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Optimization of Mixed-Integer Linear Programming Problems: A Multiparametric Optimization Approach

Pappas

Avraamidou

Katz

et al. 2021

Ind. Eng. Chem. Res.

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Industrial process systems need to be optimized, simultaneously satisfying financial, quality, and safety criteria. To meet all of those potentially conflicting optimization objectives, multiobjective optimization formulations can be used to derive optimal trade-off solutions. In this work, we present a framework that provides the exact Pareto front of multiobjective mixed-integer linear optimization problems through multiparametric programming. The original multiobjective optimization program is reformulated through the well-established ϵ-constraint scalarization method, in which the vector of scalarization parameters is treated as a right-hand side uncertainty for the multiparametric program. The algorithmic procedure then derives the optimal solution of the resulting multiparametric mixed-integer linear programming problem as an affine function of the ϵ parameters, which explicitly generates the Pareto front of the multiobjective problem. The solution of a numerical example is analytically presented to exhibit the steps of the approach, while its practicality is shown through a simultaneous process and product design problem case study. Finally, the computational performance is benchmarked with case studies of varying dimensionality with respect to the number of objective functions and decision variables.

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Multiparametric Programming in Process Systems Engineering: Recent Developments and Path Forward

Cited by 35 publications

References 167 publications

A smart manufacturing strategy for multiparametric model predictive control in air separation systems

A smart manufacturing strategy for multiparametric model predictive control in air separation systems

Multi Set-Point Explicit Model Predictive Control for Nonlinear Process Systems

Multiobjective Optimization of Mixed-Integer Linear Programming Problems: A Multiparametric Optimization Approach

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