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

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.Chemical Engineerin

Stock Management in Hospital Pharmacy using Chance-Constrained Model Predictive Control

One of the most important problems in the pharmacy department of a hospital is stock management. The clinical need for drugs must be satisfied with limited work labor while minimizing the use of economic resources. The complexity of the problem resides in the random nature of the drug demand and the multiple constraints that must be taken into account in every decision. In this article, chance-constrained model predictive control is proposed to deal with this problem. The flexibility of model predictive control allows taking into account explicitly the different objectives and constraints involved in the problem while the use of chance constraints provides a trade-off between conservativeness and efficiency. The solution proposed is assessed to study its implementation in two Spanish hospitals.Junta de Andalucía P12-TIC-240

Reliability-based economic model predictive control for generalized flow-based networks including actuators' health-aware capabilities

This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalized flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamically allocate safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the considered case study.Peer ReviewedPostprint (author's final draft

Performance optimization of a leagility inspired supply chain model: a CFGTSA algorithm based approach

Lean and agile principles have attracted considerable interest in the past few decades. Industrial sectors throughout the world are upgrading to these principles to enhance their performance, since they have been proven to be efficient in handling supply chains. However, the present market trend demands a more robust strategy incorporating the salient features of both lean and agile principles. Inspired by these, the leagility principle has emerged, encapsulating both lean and agile features. The present work proposes a leagile supply chain based model for manufacturing industries. The paper emphasizes the various aspects of leagile supply chain modeling and implementation and proposes a new Hybrid Chaos-based Fast Genetic Tabu Simulated Annealing (CFGTSA) algorithm to solve the complex scheduling problem prevailing in the leagile environment. The proposed CFGTSA algorithm is compared with the GA, SA, TS and Hybrid Tabu SA algorithms to demonstrate its efficacy in handling complex scheduling problems