arXiv subjects

Sergio Lucia

Publications and source records attributed to Sergio Lucia.

At least 19 recordsLinked to original sources

arXiv2026

Large-scale workflow placement in serverless computing using integer nonlinear programming

Serverless edge computing has become a powerful cloud framework that enables the execution of large workflows without the need for the user to manage the underlying servers and edge devices. In this work, we address the challenge of deploying these workflows on a large number of different existing servers and edge devices such that monetary costs for the users and workflow evaluation times are minimized. To this end, the workflow and cloud node attributes are modeled in a mathematical framework. As a result, we present a novel model of the optimal placement problem as a nonlinear integer program. To solve both the issues of scaling towards a larger number of cloud/edge nodes as well as decomposed knowledge of node attributes, we propose a novel decomposition strategy. In a case study, we show the beneficial scaling properties of the decomposition approach and a mean improvement of 10% against a simple deployment heuristic.

cs.DC↗

arXiv2025

Optimizing Operation Recipes with Reinforcement Learning for Safe and Interpretable Control of Chemical Processes

Optimal operation of chemical processes is vital for energy, resource, and cost savings in chemical engineering. The problem of optimal operation can be tackled with reinforcement learning, but traditional reinforcement learning methods face challenges due to hard constraints related to quality and safety that must be strictly satisfied, and the large amount of required training data. Chemical processes often cannot provide sufficient experimental data, and while detailed dynamic models can be an alternative, their complexity makes it computationally intractable to generate the needed data. Optimal control methods, such as model predictive control, also struggle with the complexity of the underlying dynamic models. Consequently, many chemical processes rely on manually defined operation recipes combined with simple linear controllers, leading to suboptimal performance and limited flexibility. In this work, we propose a novel approach that leverages expert knowledge embedded in operation recipes. By using reinforcement learning to optimize the parameters of these recipes and their underlying linear controllers, we achieve an optimized operation recipe. This method requires significantly less data, handles constraints more effectively, and is more interpretable than traditional reinforcement learning methods due to the structured nature of the recipes. We demonstrate the potential of our approach through simulation results of an industrial batch polymerization reactor, showing that it can approach the performance of optimal controllers while addressing the limitations of existing methods.

cs.LG↗

arXiv2025

Quasi-Newton Compatible Actor-Critic for Deterministic Policies

In this paper, we propose a second-order deterministic actor-critic framework in reinforcement learning that extends the classical deterministic policy gradient method to exploit curvature information of the performance function. Building on the concept of compatible function approximation for the critic, we introduce a quadratic critic that simultaneously preserves the true policy gradient and an approximation of the performance Hessian. A least-squares temporal difference learning scheme is then developed to estimate the quadratic critic parameters efficiently. This construction enables a quasi-Newton actor update using information learned by the critic, yielding faster convergence compared to first-order methods. The proposed approach is general and applicable to any differentiable policy class. Numerical examples demonstrate that the method achieves improved convergence and performance over standard deterministic actor-critic baselines.

cs.LG↗

arXiv2025

Dynamic Modeling of Precipitation in Electrolyte Systems

This study presents a dynamic modeling approach for precipitation in electrolyte systems, focusing on the crystallization of an aromatic amine through continuous processes. A novel model, integrating equilibrium and crystallization kinetics, is formulated and applied to a continuous oscillatory baffled reactor. The approach assumes rapid equilibrium establishment and is formulated as a set of differential algebraic equations. Key features include a population balance equation model to describe the particle size distribution and the modeling of dynamically changing equilibria. The predictions of the dynamic model show good agreement with the available experimental measurements. The model is aimed at aiding the transition from a batch process to continuous process by forming the basis for numerical optimization and advanced control.

physics.chem-ph↗

arXiv2025

Design of chemical recycling processes for PUR foam under uncertainty

Optimization problems in chemical process design involve a significant number of discrete and continuous decisions. When taking into account uncertainties, the search space is very difficult to explore, even for experienced engineers. Moreover, it should be taken into account that while some decisions are fixed at the design stage, other parameters can be adapted to the realization of the uncertainty during the operation of the plant. This leads to a two-stage optimization problem which is difficult to solve. To address this challenge, we propose to combine commercial process simulation software with an evolutionary strategy. This approach is applied to designing a downstream process to isolate valuable products from pyrolysis oil produced by the catalytic pyrolysis of rigid polyurethane foam. The suggested algorithm consistently performed better than a manually designed robust process. Additionally, the analysis of different scenarios provided insight into promising changes in the overall layout of the recycling process.

cs.CE↗

arXiv2025

Reverse Supply Chain Network Design of a Polyurethane Waste Upcycling System

This paper presents a general mathematical programming framework for the design and optimization of supply chain infrastructures for the upcycling of plastic waste. For this purpose, a multi-product, multi-echelon, multi-period mixed-integer linear programming (MILP) model has been formulated. The objective is to minimize the cost of the entire circular supply chain starting from the collection of post-consumer plastic waste to the production of virgin-equivalent high value polymers, satisfying a large number of constraints from collection quota to the quality of the feedstock. The framework aims to support the strategic planning of future circular supply chains by determining the optimal number, locations and sizes of various types of facilities as well as the amounts of materials to be transported between the nodes of the supply chain network over a specified period. The functionality of the framework has been tested with a case study for the upcycling of rigid polyurethane foam waste coming from construction sites in Germany. The economic potential and infrastructure requirements are evaluated, and it has been found that from a solely economic perspective, the current status of the value chain is not competitive with fossil-based feedstock or incineration. However, with the right economic incentives, there is a considerable potential to establish such value chains, once the upcycling technology is ready and the economic framework conditions have stabilized.

cs.CE↗

arXiv2025

Ellipsoidal partitions for improved multi-stage robust model predictive control

Ellipsoidal tube-based model predictive control methods effectively account for the propagation of the reachable set, typically employing linear feedback policies. In contrast, scenario-based approaches offer more flexibility in the feedback structure by considering different control actions for different branches of a scenario tree. However, they face challenges in ensuring rigorous guarantees. This work aims to integrate the strengths of both methodologies by enhancing ellipsoidal tube-based MPC with a scenario tree formulation. The uncertainty ellipsoids are partitioned by halfspaces such that each partitioned set can be controlled independently. The proposed ellipsoidal multi-stage approach is demonstrated in a human-robot system, highlighting its advantages in handling uncertainty while maintaining computational tractability.

eess.SY↗

arXiv2025

Computationally efficient Gauss-Newton reinforcement learning for model predictive control

Model predictive control (MPC) is widely used in process control due to its interpretability and ability to handle constraints. As a parametric policy in reinforcement learning (RL), MPC offers strong initial performance and low data requirements compared to black-box policies like neural networks. However, most RL methods rely on first-order updates, which scale well to large parameter spaces but converge at most linearly, making them inefficient when each policy update requires solving an optimal control problem, as is the case with MPC. While MPC policies are typically low parameterized and thus amenable to second-order approaches, existing second-order methods demand second-order policy derivatives, which can be computationally intractable. This work introduces a Gauss-Newton approximation of the deterministic policy Hessian that eliminates the need for second-order policy derivatives, enabling superlinear convergence with minimal computational overhead. To further improve robustness, we propose a momentum-based Hessian averaging scheme for stable training under noisy estimates coupled with an adaptive trustregion. We demonstrate the effectiveness of the approach on a nonlinear continuously stirred tank reactor (CSTR), showing faster convergence and improved data efficiency over state-of-the-art firstorder methods and deep RL approaches.

eess.SY↗

arXiv2025

A tutorial overview of model predictive control for continuous crystallization: current possibilities and future perspectives

This paper presents a systematic approach to the advanced control of continuous crystallization processes using model predictive control. We provide a tutorial introduction to controlling complex particle size distributions by integrating population balance equations with detailed models of various continuous crystallizers. Since these high-fidelity models are often too complex for online optimization, we propose the use of data-driven surrogate models that enable efficient optimization-based control. Through two case studies, one with a low-complexity system allowing direct comparison with traditional methods and another involving a spatially distributed crystallizer, we demonstrate how our approach enables real-time model predictive control while maintaining accuracy. The presented methodology facilitates the use of complex models in a model-based control framework, allowing precise control of key particle size distribution characteristics, such as the median particle size $d_{50}$ and the width $d_{90} - d_{10}$. This addresses a critical challenge in pharmaceutical and fine chemical manufacturing, where product quality depends on tight control of particle characteristics.

eess.SY↗

arXiv2025

Multi-Event Triggers for Serverless Computing

Function-as-a-Service (FaaS) is an event-driven serverless cloud computing model in which small, stateless functions are invoked in response to events, such as HTTP requests, new database entries, or messages. Current FaaS platform assume that each function invocation corresponds to a single event. However, from an application perspective, it is desirable to invoke functions in response to a collection of events of different types or only with every n\textsuperscript{th} event. To implement this today, a function would need additional state management, e.g., in a database, and custom logic to determine whether its trigger condition is fulfilled and the actual application code should run. In such an implementation, most function invocations would be rendered essentially useless, leading to unnecessarily high resource usage, latency, and cost for applications. In this paper, we introduce multi-event triggers, through which complex conditions for function invocations can be specified. Specifically, we introduce abstractions for invoking functions based on a set of $n$ events and joins of multiple events of different types. This enables application developers to define intricate conditions for function invocations, workflow steps, and complex event processing. Our evaluation with a proof-of-concept prototype shows that this reduces event--invocation latency by 62.5\% in an incident detection use-case and that our system can handle more than 300,000 requests per second on limited hardware, which is sufficient load for implementation in large FaaS platforms.

cs.DC↗

arXiv2025

Multi-stage model predictive control for slug flow crystallizers using uncertainty-aware surrogate models

This paper presents a novel dynamic model for slug flow crystallizers that addresses the challenges of spatial distribution without backmixing or diffusion, potentially enabling advanced model-based control. The developed model can accurately describe the main characteristics of slug flow crystallizers, including slug-to-slug variability but leads to a high computational complexity due to the consideration of partial differential equations and population balance equations. For that reason, the model cannot be directly used for process optimization and control. To solve this challenge, we propose two different approaches, conformalized quantile regression and Bayesian last layer neural networks, to develop surrogate models with uncertainty quantification capabilities. These surrogates output a prediction of the system states together with an uncertainty of these predictions to account for process variability and model uncertainty. We use the uncertainty of the predictions to formulate a robust model predictive control approach, enabling robust real-time advanced control of a slug flow crystallizer.

eess.SY↗

arXiv2024

Self-Supervised Learning of Iterative Solvers for Constrained Optimization

The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based iterative solver for constrained optimization, comprising a neural network predictor that generates initial primal-dual solution estimates, followed by a learned iterative solver that refines these estimates to reach high accuracy. We introduce a novel loss function based on Karush-Kuhn-Tucker (KKT) optimality conditions, enabling fully self-supervised training without pre-solved optimizer solutions. Theoretical guarantees ensure that the training loss function attains minima exclusively at KKT points. A convexification procedure enables application to nonconvex problems while preserving these guarantees. Experiments on two nonconvex case studies demonstrate speedups of up to one order of magnitude compared to state-of-the-art solvers such as IPOPT, while achieving orders of magnitude higher accuracy than competing learning-based approaches.

cs.LG↗

arXiv2024

On the risk levels of distributionally robust chance constrained problems

In this paper, we discuss the utilization of perturbed risk levels (PRLs) for the solution of chance-constrained problems via sampling-based approaches. PRLs allow the consideration of distributional ambiguity by rescaling the risk level of the nominal chance constraint. Explicit expressions of the PRL exist for some discrepancy-based ambiguity sets. We propose a discrepancy functional not included in previous comparisons of different PRLs based on the likelihood ratio, which we term ,,relative variation distance" (RVD). If the ambiguity set can be described by the RVD, the rescaling of the risk level with the PRL is in contrast to other discrepancy functionals possible even for very low risk levels. We derive distributionally robust one- and two-level guarantees for the solution of chance-constrained problems with randomized methods. We demonstrate the viability of the derived guarantees for a randomized MPC under distributional ambiguity.

math.OC↗

arXiv2024

Robust Model Predictive Control Exploiting Monotonicity Properties

Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between conservatism and computational complexity. Monotone systems facilitate the efficient computation of reachable sets and thus the straightforward formulation of a robust model predictive control approach optimizing over open-loop predictions. We present an approach based on the division of reachable sets to incorporate feedback in the predictions, resulting in less conservative strategies. The concept of mixed-monotonicity enables an extension of our methodology to non-monotone systems. The potential of the proposed approaches is demonstrated through a nonlinear high-dimensional chemical tank reactor cascade case study.

eess.SY↗

arXiv2024

Reinforced Model Predictive Control via Trust-Region Quasi-Newton Policy Optimization

Model predictive control can optimally deal with nonlinear systems under consideration of constraints. The control performance depends on the model accuracy and the prediction horizon. Recent advances propose to use reinforcement learning applied to a parameterized model predictive controller to recover the optimal control performance even if an imperfect model or short prediction horizons are used. However, common reinforcement learning algorithms rely on first order updates, which only have a linear convergence rate and hence need an excessive amount of dynamic data. Higher order updates are typically intractable if the policy is approximated with neural networks due to the large number of parameters. In this work, we use a parameterized model predictive controller as policy, and leverage the small amount of necessary parameters to propose a trust-region constrained Quasi-Newton training algorithm for policy optimization with a superlinear convergence rate. We show that the required second order derivative information can be calculated by the solution of a linear system of equations. A simulation study illustrates that the proposed training algorithm outperforms other algorithms in terms of data efficiency and accuracy.

cs.LG↗

arXiv2024

Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty

We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.

math.OC↗

arXiv2024

Improved uncertainty quantification for neural networks with Bayesian last layer

Uncertainty quantification is an important task in machine learning - a task in which standardneural networks (NNs) have traditionally not excelled. This can be a limitation for safety-critical applications, where uncertainty-aware methods like Gaussian processes or Bayesian linear regression are often preferred. Bayesian neural networks are an approach to address this limitation. They assume probability distributions for all parameters and yield distributed predictions. However, training and inference are typically intractable and approximations must be employed. A promising approximation is NNs with Bayesian last layer (BLL). They assume distributed weights only in the linear output layer and yield a normally distributed prediction. To approximate the intractable Bayesian neural network, point estimates of the distributed weights in all but the last layer should be obtained by maximizing the marginal likelihood. This has previously been challenging, as the marginal likelihood is expensive to evaluate in this setting. We present a reformulation of the log-marginal likelihood of a NN with BLL which allows for efficient training using backpropagation. Furthermore, we address the challenge of uncertainty quantification for extrapolation points. We provide a metric to quantify the degree of extrapolation and derive a method to improve the uncertainty quantification for these points. Our methods are derived for the multivariate case and demonstrated in a simulation study. In comparison to Bayesian linear regression with fixed features, and a Bayesian neural network trained with variational inference, our proposed method achieves the highest log-predictive density on test data.

cs.LG↗

arXiv2023

Model predictive control and moving horizon estimation for adaptive optimal bolus feeding in high-throughput cultivation of \textit{E. coli}

We discuss the application of a nonlinear model predictive control (MPC) and a moving horizon estimation (MHE) to achieve an optimal operation of \textit{E. coli} fed-batch cultivations with intermittent bolus feeding. 24 parallel experiments were considered in a high-throughput microbioreactor platform at a 10 mL scale. The robotic island in question can run up to 48 fed-batch processes in parallel with automated liquid handling and online and at-line analytics. The implementation of the model-based monitoring and control framework reveals that there are mainly three challenges that need to be addressed; First, the inputs are given in an instantaneous pulsed form by bolus injections, second, online and at-line measurement frequencies are severely imbalanced, and third, optimization for the distinctive multiple reactors can be either parallelized or integrated. We address these challenges by incorporating the concept of impulsive control systems, formulating multi-rate MHE with identifiability analysis, and suggesting criteria for deciding the reactor configuration. In this study, we present the key elements and background theory of the implementation with \textit{in silico} simulations for bacterial fed-batch cultivation.

q-bio.QM↗