Advancing Multiparametric Programming for Model Predictive Control

Model predictive control provides the optimal operation for chemical processes by explicitly accounting for the system, constraints, and costs. In an online setting, developing the implicit optimal control action under time consideration is non-trivial. Over a decade ago, it was demonstrated through multiparametric programming that the implicit control law defining the model predictive controller can be determined explicitly, once and offline. The benefit of such an approach is the (i) improved online computational time, (ii) the development of the offline map of solution \textit{a priori}, and (iii) the derivation of the optimal control laws under any state variation. In recent years there has been a significant push for the development of novel algorithms and theoretical advancements for multiparametric model predictive control. These algorithms and theoretical underpinnings have expanded the problem classes that are solvable and improved the computational efficiency. However, there is still a need to provide analysis for formulations based on different surrogate models, and to tackle large scale multiparametric model predictive control problems. In this dissertation, the research focus is (i) the inclusion of a new surrogate modeling technique from the machine learning community, (ii) developing a criterion to compare multiparametric model predictive control formulations based on different surrogate models, (iii) the development of an algorithm to solve large scale multiparametric optimization problems, and (iv) improving the online computational performance of online solvers via multiparametric programming. To this end, tools from data science, computational geometry, and the operations research community contributed greatly to the results presented in this work. This research is verified via the optimal operation of chemical engineering processes and the efficacy of the developed algorithms is demonstrated on computational studies

Advances in the Optimization of Energy Systems and Machine Learning Hyperparameters

Intensifying public concern about climate change risks has accelerated the push for more tangible action in the transition toward low-carbon or carbon-neutral energy. Concurrently, the energy industry is also undergoing a digital transformation with the explosion in available data and computational power. To address these challenges, systematic decision-making strategies are necessary to analyze the vast array of technology options and information sources while navigating this energy transition. In this work, mathematical optimization is utilized to answer some of the outstanding issues around designing cleaner processes from resources such as natural gas and renewables, operating the logistics of these energy systems, and statistical modeling from data. First, exploiting natural gas to produce lower emission liquid transportation fuels is investigated through an optimization-based process synthesis. This extends previous studies by incorporating chemical looping as an alternative syngas production method for the first time. Second, a similar process synthesis approach is implemented for the optimal design of a novel biomass-based process that coproduces ammonia and methanol, improving their production flexibility and profit margins. Next, operational difficulties with solar and wind energies due to their temporal intermittency and uneven geographical distribution are tackled with a supply chain optimization model and a clustering decomposition algorithm. The former describes power generation through energy carriers (hydrogen-rich chemicals) connecting resource-dense rural areas to resource-deficient urban centers. Results show the potential of energy carriers for long-term storage. The latter is developed to identify the appropriate number of representative time periods for approximating an optimization problem with time series data, instead of using a full time horizon. This algorithm is applied to the simultaneous design and scheduling of a renewable power system with battery storage. Finally, building machine learning models from data is commonly performed through k-fold cross-validation. From recasting this as a bilevel optimization, the exact solution to hyperparameter optimization is obtainable through parametric programming for machine learning models that are LP/QP. This extends previous results in statistics to a broader class of machine learning models

Advances in Data-Driven Modeling and Global Optimization of Constrained Grey-Box Computational Systems

The effort to mimic a chemical plant’s operations or to design and operate a completely new technology in silico is a highly studied research field under process systems engineering. As the rising computation power allows us to simulate and model systems in greater detail through careful consideration of the underlying phenomena, the increasing use of complex simulation software and generation of multi-scale models that spans over multiple length and time scales calls for computationally efficient solution strategies that can handle problems with different complexities and characteristics. This work presents theoretical and algorithmic advancements for a range of challenging classes of mathematical programming problems through introducing new data-driven hybrid modeling and optimization strategies. First, theoretical and algorithmic advances for bi-level programming, multi-objective optimization, problems containing stiff differential algebraic equations, and nonlinear programming problems are presented. Each advancement is accompanied with an application from the grand challenges faced in the engineering domain including, food-energy-water nexus considerations, energy systems design with economic and environmental considerations, thermal cracking of natural gas liquids, and oil production optimization. Second, key modeling challenges in environmental and biomedical systems are addressed through employing advanced data analysis techniques. Chemical contaminants created during environmental emergencies, such as hurricanes, pose environmental and health related risks for exposure. The goal of this work is to alleviate challenges associated with understanding contaminant characteristics, their redistribution, and their biological potential through the use of data analytics