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Multiparametric Optimization Strategies for Process Operations Under Uncertainty
Abstract
The presence of uncertainty is ubiquitous in the operation of processes, due to their time-varying inherent characteristics, external effects that disturb their nominal behavior, and their imperfect description with mathematical models. This dissertation is concerned with the development and application of multiparametric programming-based techniques for the optimization of the operation of process systems under uncertainty.
Firstly, an exact strategy that solves multiparameric quadratically constrained quadratic programming problems is presented, which is founded on a second-order Taylor approximation of the Basic Sensitivity Theorem. The proposed approach is applied to numerical case studies, model predictive control, and flexibility analysis problems.
For general multiparametric nonlinear programming problems, a framework for the incorporation of deep neural networks with rectified linear units is proposed. An exact reformulation of the neural network to a multiparametric mixed-integer linear programming problem is achieved, which can be solved with off-the-shelf solvers. Applications of this framework include the regulation of a solar field and a bioreactor.
Furthermore, inspired by the multiobjective nature of optimization problems, and the aforementioned development of modeling complex processes with data-driven models, a framework for the solution of multiobjective mixed-integer linear programming problems is presented. The utilization of this framework allows for the exact and explicit derivation of the Pareto front of the problem a priori. A simultaneous product and process design and a scheduling application are utilized to exhibit the benefits of the strategy.
An algorithm that derives robust explicit control policies for model predictive control applications is also proposed. Discrete linear models are considered, with assumed multiplicative uncertainty intervals belonging to a box uncertainty set. Robust optimization techniques are adopted to guarantee feasibility of the problem that allow for the explicit solution of model predictive control problems with a quadratic cost function and linear constraints with a single problem formulation.
Finally, two applications of multiparametric programming for the optimal operation of intensified processes are presented. The regulation of an industrial application of a dividing wall column that purifies methyl methacrylate, as well as the simultaneous design and control of reactive distillation column that produces methyl tert-butyl ether.
Subject
multiparametric optimizationoptimization under uncertainty
model predictive control
process operations
Citation
Pappas, Iosif (2022). Multiparametric Optimization Strategies for Process Operations Under Uncertainty. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /197992.