Moving horizon optimization methods, applications and tools for learning and controlling dynamical systems

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2023-05

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Abstract

Mathematical models based on dynamical systems are crucial for understanding complex phenomena across a wide range of scientific and engineering disciplines. Optimizing these models can significantly improve the performance (e.g., in the sense of socioeconomic, environmental, and safety concerns) of various processes and systems that support our modern society, such as e.g. supply chain networks and chemical manufacturing processes. However, controlling these systems in the presence of uncertainty and for high-dimensional models is challenging. Developing robust and efficient optimization models and solution algorithms for this purpose is therefore crucial. Similarly, optimization techniques can be used to infer the governing equations for such dynamical systems from available measurement data. Learning such models is important not only for performing the aforementioned control tasks, but also for advancing our understanding of the physical laws that govern the phenomena we have so long observed but cannot quantitatively explain. Motivated by the above, this dissertation contributes novel moving horizon optimization methods, applications and tools for learning and controlling a variety of dynamical systems. The first part of this dissertation introduces the background and theory of moving horizon estimation and control methods. As a motivating example, I present a novel application of these existing methods to the optimal data-driven management of the COVID-19 pandemic in the US. The proposed approach identifies optimal social distancing and testing policies that minimize socioeconomic impact, while keeping the the number of infected individuals under a specified threshold. Subsequently, I focus on dynamical system models corresponding networks of integrators for optimal supply chain management under uncertainty. The first methodological contribution corresponds to a tube-based robust economic model predictive control framework for sparse storage systems, which I shown to have improved feasibility for supply chain management under demand disturbances. The proposed approach significantly improves computational performance relative to the available methods. Subsequently, I develop an extensive and systematic case study evaluating the performance of deterministic (feedback-based, closed-loop, or online) moving horizon optimization in comparison to stochastic and robust methods for supply chain management under increasing levels of uncertainty, forecasting errors, and recourse availability.
Having demonstrated the overall robust and computationally efficient performance of deterministic moving horizon optimization techniques, the second part of the dissertation is focused on a class of multi-scale dynamical systems corresponding to supply chains of highly perishable inventory. This type of supply chains require integration of the inventory management problem with quality control by manipulating environmental conditions (e.g., temperature) during shipment and storage, which directly impact the product deterioration rate. To this end, I introduce a novel modeling approach for incorporating complex, multivariate physico-chemical product quality dynamics within the supply chain inventory balances, and provide a computationally efficient reformulation thereof. Based on this modeling approach and the results introduced in Part I of the dissertation, I develop a stabilizing closed-loop optimal supply chain production and distribution planning framework to handle uncertainties, such as random customer demand and/or random product quality spoilage. I then propose a scalable solution heuristic approach to cope with larger supply chain networks, and I present several case studies to demonstrate robustness to demand uncertainty. Lastly, I develop a simultaneous state estimation and closed-loop control approach to account for the fact that product quality may not be completely measurable in practical settings. In the third and final part of the dissertation, the focus shifts from controlling dynamical systems to learning their governing equations from data via moving horizon optimization. Here, I develop methods based on dynamic nonlinear optimization which, compared to existing efforts, demonstrate greater flexibility for handling highly nonlinear systems, for incorporating prior domain knowledge, and coping with high amounts of measurement noise in the training data. I then demonstrate the extension of this learning framework to the case of reactive dynamical system and present numerical experiments for non-isothermal continuous and batch chemical reactors. Lastly, I develop a sequential dynamic nonlinear optimization approach for discovering and performing dimensionality reduction of microkinetic reaction networks.

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