arXiv subjects

Rolf Findeisen

Publications and source records attributed to Rolf Findeisen.

At least 37 records · Page 2Linked to original sources

arXiv2025

Energy Aware and Safe Path Planning for Unmanned Aircraft Systems

This paper proposes a path planning algorithm for multi-agent unmanned aircraft systems (UASs) to autonomously cover a search area, while considering obstacle avoidance, as well as the capabilities and energy consumption of the employed unmanned aerial vehicles. The path planning is optimized in terms of energy efficiency to prefer low energy-consuming maneuvers. In scenarios where a UAS is low on energy, it autonomously returns to its initial position for a safe landing, thus preventing potential battery damage. To accomplish this, an energy-aware multicopter model is integrated into a path planning algorithm based on model predictive control and mixed integer linear programming. Besides factoring in energy consumption, the planning is improved by dynamically defining feasible regions for each UAS to prevent obstacle corner-cutting or over-jumping.

eess.SY↗

arXiv2025

Exploiting Prior Knowledge in Preferential Learning of Individualized Autonomous Vehicle Driving Styles

Trajectory planning for automated vehicles commonly employs optimization over a moving horizon - Model Predictive Control - where the cost function critically influences the resulting driving style. However, finding a suitable cost function that results in a driving style preferred by passengers remains an ongoing challenge. We employ preferential Bayesian optimization to learn the cost function by iteratively querying a passenger's preference. Due to increasing dimensionality of the parameter space, preference learning approaches might struggle to find a suitable optimum with a limited number of experiments and expose the passenger to discomfort when exploring the parameter space. We address these challenges by incorporating prior knowledge into the preferential Bayesian optimization framework. Our method constructs a virtual decision maker from real-world human driving data to guide parameter sampling. In a simulation experiment, we achieve faster convergence of the prior-knowledge-informed learning procedure compared to existing preferential Bayesian optimization approaches and reduce the number of inadequate driving styles sampled.

eess.SY↗

arXiv2025

Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.

eess.SY↗

arXiv2024

Interpretation of High-Dimensional Regression Coefficients by Comparison with Linearized Compressing Features

Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data, motivated by predicting cycle life for lithium-ion batteries. We develop a linearization method to derive feature coefficients, which we compare with the closest regression coefficients of the path of regression solutions. We showcase the methods on battery data case studies where a single nonlinear compressing feature, $g\colon \mathbb{R}^p \to \mathbb{R}$, is used to construct a synthetic response, $\mathbf{y} \in \mathbb{R}$. This unifying view of linear regression and compressing features for high-dimensional functional data helps to understand (1) how regression coefficients are shaped in the highly regularized domain and how they relate to linearized feature coefficients and (2) how the shape of regression coefficients changes as a function of regularization to approximate nonlinear responses by exploiting local structures.

cs.LG↗

arXiv2024

Gaussian process-based online health monitoring and fault analysis of lithium-ion battery systems from field data

Health monitoring, fault analysis, and detection are critical for the safe and sustainable operation of battery systems. We apply Gaussian process resistance models on lithium iron phosphate battery field data to effectively separate the time-dependent and operating point-dependent resistance. The data set contains 29 battery systems returned to the manufacturer for warranty, each with eight cells in series, totaling 232 cells and 131 million data rows. We develop probabilistic fault detection rules using recursive spatiotemporal Gaussian processes. These processes allow the quick processing of over a million data points, enabling advanced online monitoring and furthering the understanding of battery pack failure in the field. The analysis underlines that often, only a single cell shows abnormal behavior or a knee point, consistent with weakest-link failure for cells connected in series, amplified by local resistive heating. The results further the understanding of how batteries degrade and fail in the field and demonstrate the potential of efficient online monitoring based on data. We open-source the code and publish the large data set upon completion of the review of this article.

cs.LG↗

arXiv2024

Probabilistically Input-to-State Stable Stochastic Model Predictive Control

Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated feasibility guarantees for standard stochastic MPC formulations. Thus, traditional stability proofs are not straightforwardly applicable. We exploit the concept of input-to-state stability in probability and outline how it can be used to provide stability guarantees, circumventing the requirement for strict repeated feasibility guarantees. Loss of feasibility is captured by a back-up controller, which is explicitly taken into account in the stability analysis. We illustrate our findings using a numeric example.

eess.SY↗

arXiv2024

Safe Learning-Based Optimization of Model Predictive Control: Application to Battery Fast-Charging

Model predictive control (MPC) is a powerful tool for controlling complex nonlinear systems under constraints, but often struggles with model uncertainties and the design of suitable cost functions. To address these challenges, we discuss an approach that integrates MPC with safe Bayesian optimization to optimize long-term closed-loop performance despite significant model-plant mismatches. By parameterizing the MPC stage cost function using a radial basis function network, we employ Bayesian optimization as a multi-episode learning strategy to tune the controller without relying on precise system models. This method mitigates conservativeness introduced by overly cautious soft constraints in the MPC cost function and provides probabilistic safety guarantees during learning, ensuring that safety-critical constraints are met with high probability. As a practical application, we apply our approach to fast charging of lithium-ion batteries, a challenging task due to the complicated battery dynamics and strict safety requirements, subject to the requirement to be implementable in real time. Simulation results demonstrate that, in the context of model-plant mismatch, our method reduces charging times compared to traditional MPC methods while maintaining safety. This work extends previous research by emphasizing closed-loop constraint satisfaction and offers a promising solution for enhancing performance in systems where model uncertainties and safety are critical concerns.

eess.SY↗

arXiv2024

Safe and Stable Closed-Loop Learning for Neural-Network-Supported Model Predictive Control

Safe learning of control policies remains challenging, both in optimal control and reinforcement learning. In this article, we consider safe learning of parametrized predictive controllers that operate with incomplete information about the underlying process. To this end, we employ Bayesian optimization for learning the best parameters from closed-loop data. Our method focuses on the system's overall long-term performance in closed-loop while keeping it safe and stable. Specifically, we parametrize the stage cost function of an MPC using a feedforward neural network. This allows for a high degree of flexibility, enabling the system to achieve a better closed-loop performance with respect to a superordinate measure. However, this flexibility also necessitates safety measures, especially with respect to closed-loop stability. To this end, we explicitly incorporated stability information in the Bayesian-optimization-based learning procedure, thereby achieving rigorous probabilistic safety guarantees. The proposed approach is illustrated using a numeric example.

eess.SY↗

arXiv2024

Neural Horizon Model Predictive Control -- Increasing Computational Efficiency with Neural Networks

The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach addresses this by utilizing a feed-forward neural network to reduce the computation load of the online-optimization. We propose approximating part of the problem horizon, while maintaining safety guarantees -- constraint satisfaction -- via the remaining optimization part of the controller. The approach is validated in simulation, demonstrating an improvement in computational efficiency, while maintaining guarantees and near-optimal performance. The proposed MPC scheme can be applied to a wide range of applications, including those requiring a rapid control response, such as robotics and embedded applications with limited computational resources.

eess.SY↗

arXiv2024

Accounting for the Effects of Probabilistic Uncertainty During Fast Charging of Lithium-ion Batteries

Batteries are nonlinear dynamical systems that can be modeled by Porous Electrode Theory models. The aim of optimal fast charging is to reduce the charging time while keeping battery degradation low. Most past studies assume that model parameters and ambient temperature are a fixed known value and that all PET model parameters are perfectly known. In real battery operation, however, the ambient temperature and the model parameters are uncertain. To ensure that operational constraints are satisfied at all times in the context of model-based optimal control, uncertainty quantification is required. Here, we analyze optimal fast charging for modest uncertainty in the ambient temperature and 23 model parameters. Uncertainty quantification of the battery model is carried out using non-intrusive polynomial chaos expansion and the results are verified with Monte Carlo simulations. The method is investigated for a constant current--constant voltage charging strategy for a battery for which the strategy is known to be standard for fast charging subject to operating below maximum current and charging constraints. Our results demonstrate that uncertainty in ambient temperature results in violations of constraints on the voltage and temperature. Our results identify a subset of key parameters that contribute to fast charging among the overall uncertain parameters. Additionally, it is shown that the constraints represented by voltage, temperature, and lithium-plating overpotential are violated due to uncertainties in the ambient temperature and parameters. The C-rate and charge constraints are then adjusted so that the probability of violating the degradation acceleration condition is below a pre-specified value. This approach demonstrates a computationally efficient approach for determining fast-charging protocols that take probabilistic uncertainties into account.

eess.SY↗

arXiv2024

Geometric Data-Driven Dimensionality Reduction in MPC with Guarantees

We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at identifying a suboptimal solution within a low-dimensional subspace, retains the stability and recursive feasibility characteristics of the original problem. We present a necessary and sufficient condition for ensuring initial feasibility, which is seamlessly integrated into the subspace design process. Additionally, we employ techniques from optimization on Riemannian manifolds to develop a subspace that efficiently represents a collection of pre-specified high-dimensional data points, all while adhering to the initial admissibility constraint.

eess.SY↗

arXiv2024

Stability-informed Bayesian Optimization for MPC Cost Function Learning

Designing predictive controllers towards optimal closed-loop performance while maintaining safety and stability is challenging. This work explores closed-loop learning for predictive control parameters under imperfect information while considering closed-loop stability. We employ constrained Bayesian optimization to learn a model predictive controller's (MPC) cost function parametrized as a feedforward neural network, optimizing closed-loop behavior as well as minimizing model-plant mismatch. Doing so offers a high degree of freedom and, thus, the opportunity for efficient and global optimization towards the desired and optimal closed-loop behavior. We extend this framework by stability constraints on the learned controller parameters, exploiting the optimal value function of the underlying MPC as a Lyapunov candidate. The effectiveness of the proposed approach is underlined in simulations, highlighting its performance and safety capabilities.

eess.SY↗

arXiv2024

Learning Model Predictive Control Parameters via Bayesian Optimization for Battery Fast Charging

Tuning parameters in model predictive control (MPC) presents significant challenges, particularly when there is a notable discrepancy between the controller's predictions and the actual behavior of the closed-loop plant. This mismatch may stem from factors like substantial model-plant differences, limited prediction horizons that do not cover the entire time of interest, or unforeseen system disturbances. Such mismatches can jeopardize both performance and safety, including constraint satisfaction. Traditional methods address this issue by modifying the finite horizon cost function to better reflect the overall operational cost, learning parts of the prediction model from data, or implementing robust MPC strategies, which might be either computationally intensive or overly cautious. As an alternative, directly optimizing or learning the controller parameters to enhance closed-loop performance has been proposed. We apply Bayesian optimization for efficient learning of unknown model parameters and parameterized constraint backoff terms, aiming to improve closed-loop performance of battery fast charging. This approach establishes a hierarchical control framework where Bayesian optimization directly fine-tunes closed-loop behavior towards a global and long-term objective, while MPC handles lower-level, short-term control tasks. For lithium-ion battery fast charging, we show that the learning approach not only ensures safe operation but also maximizes closed-loop performance. This includes maintaining the battery's operation below its maximum terminal voltage and reducing charging times, all achieved using a standard nominal MPC model with a short horizon and notable initial model-plant mismatch.

eess.SY↗

arXiv2024

Cycle Life Prediction for Lithium-ion Batteries: Machine Learning and More

Batteries are dynamic systems with complicated nonlinear aging, highly dependent on cell design, chemistry, manufacturing, and operational conditions. Prediction of battery cycle life and estimation of aging states is important to accelerate battery R&D, testing, and to further the understanding of how batteries degrade. Beyond testing, battery management systems rely on real-time models and onboard diagnostics and prognostics for safe operation. Estimating the state of health and remaining useful life of a battery is important to optimize performance and use resources optimally. This tutorial begins with an overview of first-principles, machine learning, and hybrid battery models. Then, a typical pipeline for the development of interpretable machine learning models is explained and showcased for cycle life prediction from laboratory testing data. We highlight the challenges of machine learning models, motivating the incorporation of physics in hybrid modeling approaches, which are needed to decipher the aging trajectory of batteries but require more data and further work on the physics of battery degradation. The tutorial closes with a discussion on generalization and further research directions.

eess.SY↗

arXiv2024

Regret and Conservatism of Distributionally Robust Constrained Stochastic Model Predictive Control

We analyse the conservatism and regret of distributionally robust (DR) stochastic model predictive control (SMPC) when using moment-based ambiguity sets for modeling unknown uncertainties. To quantify the conservatism, we compare the deterministic constraint tightening while taking a DR approach against the optimal tightening when the exact distributions of the stochastic uncertainties are known. Furthermore, we quantify the regret by comparing the performance when the distributions of the stochastic uncertainties are known and unknown. Analysing the accumulated sub-optimality of SMPC due to the lack of knowledge about the true distributions of the uncertainties marks the novel contribution of this work.

eess.SY↗

arXiv2024

Experimentally implemented dynamic optogenetic optimization of ATPase expression using knowledge-based and Gaussian-process-supported models

Optogenetic modulation of adenosine triphosphatase (ATPase) expression represents a novel approach to maximize bioprocess efficiency by leveraging enforced adenosine triphosphate (ATP) turnover. In this study, we experimentally implement a model-based open-loop optimization scheme for optogenetic modulation of the expression of ATPase. Increasing the intracellular concentration of ATPase, and thus the level of ATP turnover, in bioprocesses with product synthesis coupled with ATP generation, can lead to increased product formation and substrate uptake. Previous simulation studies formulated optimal control problems using dynamic constraint-based models to find optimal light inputs in fermentations with optogenetically mediated ATPase expression. However, using these models poses challenges due to resulting bilevel optimizations and complex parameterization. Here, we outline a simplified unsegregated and quasi-unstructured kinetic modeling approach that reduces the number of dynamic states and leads to single-level optimizations. The models can be augmented with Gaussian processes to compensate for model uncertainties. We implement optimal control constrained by knowledge-based and hybrid models for optogenetic ATPase expression in $\textit{Escherichia coli}$ with lactate as the main product. To do so, we genetically engineer $\textit{E. coli}$ to obtain optogenetic expression of ATPase using the CcaS/CcaR system. This represents the first experimental implementation of model-based optimization of ATPase expression in bioprocesses.

eess.SY↗

arXiv2023

The electrostatic potential of atomic nanostructures on a metal surface

The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and are determined by their shape, material, and environment. Such fields are relevant in catalysis, nanoelectronics and quantum nanoscience, and their control will become even more important as the devices in question reach few-nanometres dimensions. Surface-averaging techniques provide only limited experimental access to these potentials at and around individual nanostructures. Here, we use scanning quantum dot microscopy to investigate how electric potentials evolve as nanostructures are built up atom by atom. We image the potential over adatoms, chains, and clusters of Ag and Au atoms on Ag(111) and quantify their surface dipole moments. By focusing on the total charge density, these data establish a new benchmark for ab initio calculations. Indeed, our density functional theory calculations not only show an impressive agreement with experiment, but also allow a deeper analysis of the mechanisms behind the dipole formation, their dependence on fundamental atomic properties and on the atomic configuration of the nanostructures. This allows us to formulate an intuitive picture of the basic mechanisms behind dipole formation, which enables better design choices for future nanoscale systems such as single atom catalysts.

cond-mat.mtrl-sci↗

arXiv2023

Interpretation of High-Dimensional Linear Regression: Effects of Nullspace and Regularization Demonstrated on Battery Data

High-dimensional linear regression is important in many scientific fields. This article considers discrete measured data of underlying smooth latent processes, as is often obtained from chemical or biological systems. Interpretation in high dimensions is challenging because the nullspace and its interplay with regularization shapes regression coefficients. The data's nullspace contains all coefficients that satisfy $\mathbf{Xw}=\mathbf{0}$, thus allowing very different coefficients to yield identical predictions. We developed an optimization formulation to compare regression coefficients and coefficients obtained by physical engineering knowledge to understand which part of the coefficient differences are close to the nullspace. This nullspace method is tested on a synthetic example and lithium-ion battery data. The case studies show that regularization and z-scoring are design choices that, if chosen corresponding to prior physical knowledge, lead to interpretable regression results. Otherwise, the combination of the nullspace and regularization hinders interpretability and can make it impossible to obtain regression coefficients close to the true coefficients when there is a true underlying linear model. Furthermore, we demonstrate that regression methods that do not produce coefficients orthogonal to the nullspace, such as fused lasso, can improve interpretability. In conclusion, the insights gained from the nullspace perspective help to make informed design choices for building regression models on high-dimensional data and reasoning about potential underlying linear models, which are important for system optimization and improving scientific understanding.

stat.ML↗