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At least 307 records · Page 17

Data-model files associated with the manuscript "Modeling the Effects of Wetland Restoration on Coastal Hydrology: A Case Study of Elkhorn Slough Watershed, California"

This package contains the data, simulation setups, notebooks and figures used in “Modeling the Effects of Wetland Restoration on Coastal Hydrology: A Case Study of Elkhorn Slough Watershed, California” (Xu et al., 2025). In this study, we selected Elkhorn Slough, a tidal estuary, in California, to investigate the impact of wetland restoration and sea level rise on coastal hydrology using the process-based coastal hydrologic model, Advanced Terrestrial Simulator (ATS), informed by site-specific data. We designed a novel modeling workflow for incorporating wetland restoration features into land cover and soil properties for the model parameterization. The validation results demonstrate a strong agreement between modeled and observed data. We studied the characteristics of coastal watershed hydrology, then focused on the surface water dynamics at two wetland sites within Elkhorn Slough, a reference site and a restored site. Our simulation results indicate that the restored site successfully maintains surface elevation, resulting in reduced surface inundation. We also examined the impact of wetland restoration under expected sea level rise over the next few decades. The low-lying Yampah Marsh, the reference site, is likely to be inundated due to future sea level rise when highest tides arrive; while a higher percentage of Hester Marsh, the restored site, would retain marsh vegetation in coming decades, regardless of tidal conditions. Our study provides important information for examining the outcome of restoration practices that include surface elevation in tidal wetlands under climate changes.Several files can be found from this data package.1. README.md: This file describes the title, journal, co-authors, abstract, repository structure and model version.2. Simulation_Setups.zip: The file contains the model configuration files (XML format) for ATS. 3. Notebooks.zip: The file contains the Jupyter notebooks for generating the pre- and post-restoration meshes and the meshes of future scenarios. 4. Figures.zip: The file contains the figures used in the manuscript.5. Data.zip: The file contains the data used to drive the model simulations, including watershed and wetlands boundaries, mesh files and references to additional datasets (e.g., meteorological forcing, tidal dataset, DEMs, land cover, soil properties). Also, it contains water level observations at the restored wetland.

54 ENVIRONMENTAL SCIENCES↗

Dynamic Data-Driven Multiscale Modeling for Predicting Microstructure and Mechanical Properties of 316L Stainless Steel

We have developed a long short-term memory stacked ensemble (LSTM-SE) surrogate modeling approach that can provide rapid predictions of microstructural evolution and the resultant mechanical properties of American Iron and Steel Institute (AISI) 316L series stainless steel (316LSS) fuel cladding under conditions of varying temperature and radiation dose rate. To acquire training data, we developed and implemented a kinetic Monte Carlo (KMC) model to simulate precipitation kinetics of M 23 C 6 , γ', and G phases within SS316L cladding. Experimentally reported precipitation kinetics of SS316L in literature were linked to the kinetic parameters of the simulated precipitation in our KMC model. The model was then used to simulate microstructure evolution under synthetically generated treatments of varying temperature and radiation dose rate, for periods of up to 3000 hours. Changes in volume fraction, number density, and particle size of precipitates were recorded, and particle area fractions were correlated using statistical methods to develop the surrogate model. Simultaneously, the mechanical properties of the simulated microstructures were evaluated using microstructure-based finite element method (FEM) analysis to determine the elastic modulus, yield stress, ultimate tensile strength, and elongation to failure of the aged microstructures. Using this approach, our surrogate model can predict precipitation behavior within 0.25% volume fraction and mechanical properties within 6% relative error from the values predicted by the KMC and FEM models using 50 training simulations as input. The trained recurrent neural network-based model can return estimations of precipitation kinetics and mechanical properties ~1000 times faster than the physics-based codes. This work demonstrates, as a proof of concept, that reactor material service lifetimes under variable service conditions can be predicted for a statistics-based model from a practicably obtainable dataset.

36 MATERIALS SCIENCE↗

Model-based Hierarchical Reinforcement Learning for Improved Physical Security Design: A Prototype

Prior work in FY24 developed an adversarial AI agent aid in path analysis of physical protection systems. This agent, trained using a model-based reinforcement learning algorithm, was able to successfully learn the most vulnerable path in facilities. It was able to extend the current state of practice for physical protection design by exhibiting dynamic behavior based on current environmental conditions. Whereas PathTrace largely performs a static, graph-based analysis, the AI agent was able to make decisions based on relative position in the facility, current conditions (was the adversarial agnet discovered?), and proximity to secondary targets. The agent demonstrated some novel capabilities, but had limitations that need to be resolved before it can be used for production purposes. For example, the adversarial agent generalizes poorly and takes a relatively long time to train. Nonetheless, there is still considerable promise for developing the adversarial agent further in order to explore even richer, more dynamic behaviors (e.g., adversary motivations, environmental debris, and more). This work considers a complementary idea; development of a planning agent. The planning agent is envisioned as an auto-complete-like tool that can help accelerate security system design by human experts. The agent would respect existing barriers and sensors placed by a human expert while offering cost-effective suggestions (i.e., implicitly balancing effectiveness with cost) to improve the design. The goal is for this agent to be part of an expert’s toolbox, not to totally upend the current state-of-practice, or to displace human experts. The ultimate goal would be concurrent training of both the adversarial and planning agent together, to learn entirely through self-play. This would represent an entirely new way of performing system deign. We selected a hierarchical, model-based reinforcement learning algorithm to serve as the planning agent. This is an extension of concepts used in the prior FY24 adversarial agent work. There, we had a single agent acting an environment. Here, we have two different sub-agents (policies), working together, to form a complete agent. There is a manager policy, which can select abstract goals on slower time scales, and a worker, which performs primitive actions to reach goals selected by the manager. It is worth noting that this class of algorithm is challenging to work with. From our understanding, our work is one of the first successful uses of model-based reinforcement learning (MBRL) in nuclear energy1 , and likely the first hierarchical model-based reinforcement learning application in nuclear energy. Further, this work is one of the first known attempts to apply AI to perform a design tasks in nuclear energy. Consequently, there were significant implementation challenges and the bulk of the work was focused on successful implementation and algorithm design. The results presented here are very low technology readiness level as a consequence of the lack of related literature, but still represent a significant step forward in the pursuit of applied AI for design.

42 ENGINEERING↗

Double-Shell Tank Primary Bottom Visual Inspection Results - 20025

A pressing need for the Double-Shell Tank Integrity Program at Hanford is of the ability to inspect the bottom of the tanks. Though the DSTs' annulus spaces (the space between the internal and external tank walls) have been inspected visually since 1992 and with Ultrasonic Testing (UT) since 1996, inspections of the tank bottoms have been able to be conducted due to limitations of available technology, omitting about 40 percent of the tank surface below the maximum fill level from routine inspection. Visual inspections of the tank annulus have been conducted up to five times in some DSTs and portions of the annulus space for all of the DSTs has been inspected twice with UT. This region includes the walls of the primary tank and secondary liner along with accessible portions of the secondary liner bottom. Due to this lack of technology, the degradation of the primary tank bottom in Tank AY-102 was undetected until the tank leaked into its annulus space, confirmed in 2012. Since that time, WRPS has been working with the nondestructive examination community and the Pacific Northwest National Laboratory, to evaluate potential technologies to conduct these challenging remote inspections. Recent work has included the development, testing, and deployment of several remote visual inspection technologies to observe the condition of the primary tank bottom of the DSTs by leveraging air distribution slots in the refractory pad on which it rests. Robotic solutions to conduct this inspection were developed with a detailed understanding of the physical configuration and operational logistics. Understanding and subsequent communication of these details to vendors within the robotics and nondestructive examination community was a critical component to the successful production of these new tools. Throughout the FY16-FY18 years, vendors from nondestructive examination community were solicited for ideas to meet the tank bottom inspection challenge. Two tank bottom visual inspection solutions were then pursued to meet that challenge. Both tools were successfully deployed at Tank AP-107, and provided valuable visuals, never before obtained from the under tank environment of a double-shell tank. While there are minor opportunities for improvement identified with each system, general outcomes were overwhelmingly positive. Both systems were successfully able to navigate the refractory air slot pattern from the outer edge to the tank center and record video footage. The micro-crawler provided high quality and very stable footage through the air slot pattern, but took longer to deploy into the slots and traverse through them than the alternative system. The push-pull tethered camera was able to navigate all seven of its target air slots in a matter of a few hours, which included deployment, movement between slot entrances, and complete removal of the system from the annulus environment. Through these air slots, new information was gained about the tank bottom and refractory pad condition of tank AP-107, AP-106, AP-108, and AN-102. While some debris was noted in the air slots, including sand, chipped refractory, and construction materials, the refractory was found to be structurally stable and adequately supporting the primary tank bottom through the full diameter of the tank. Primary tank bottom steel exterior was found to be in good condition, free of ongoing or aggressive corrosion conditions. Looking toward the future, robotic access to and visual inspection of refractory air slots and the primary tank bottom steel has now proven viable. Incorporating periodic air slot inspections as a regular practice within the Double-Shell Tank Integrity Program is the next step, allowing trending of any changes in condition. As ultrasonic testing infrastructure was leveraged to complete the initial system deployments described in this report, it makes sense to adopt that same strategy for ongoing periodic examinations and deploy these primary tank bottom inspection tools alongside ultrasonic testing operations. Development of visual inspection tools to evaluate the primary tank bottom region of the double-shell tanks was planned as the first stage of inspection. Continued development of volumetric sensors and incorporation of these inspection tools into Hanford's ongoing Double-Shell Tank Integrity Program are the next steps, seeking to continuously expand understanding of asset integrity and remaining useful life. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

An Evaluation of Sustainable Power System Resilience in the Face of Severe Weather Conditions and Climate Changes: A Comprehensive Review of Current Advances

Natural disasters pose significant threats to power distribution systems, intensified by the increasing impacts of climate changes. Resilience-enhancement strategies are crucial in mitigating the resulting social and economic damages. Hence, this review paper presents a comprehensive exploration of weather management strategies, augmented by recent advancements in machine learning algorithms, to show a sustainable resilience assessment. By addressing the unique challenges posed by diverse weather conditions, we propose flexible and intelligent solutions to navigate disaster complications effectively. This proposition emphasizes sustainable practices that not only address immediate disaster complications, but also prioritize long-term resilience and adaptability. Furthermore, the focus extends to mitigation strategies and microgrid technologies adapted to distribution systems. Through statistical analysis and mathematical formulations, we highlight the critical role of these advancements in mitigating severe weather conditions and ensuring the system reliability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Opportunities for iron and steel industrial wastewater treatment and reuse in the United States

Concerns around water security in the United States have heightened the interest in industrial water treatment and reuse to improve water efficiency and operational reliability. Alongside nationwide efforts to expand industrial capacity, primary manufacturing sectors are adopting more resource-efficient technologies. This transition is expected to shift industrial water consumption patterns, driving the need for improved treatment and reuse practices. This study investigates opportunities for water use, treatment, and reuse in the iron and steel sector through a review of academic and industry literature and interviews with industry representatives. It identifies key challenges in water and wastewater management and outlines the conditions under which innovative treatment technologies could be deployed. Based on these insights, the study presents a practical water management action plan. Furthermore, it assesses water quality targets across different process operations, evaluates existing treatment technologies, and highlights challenges and opportunities for improvement relative to future performance expectations. Although water is often perceived as a low-cost commodity, industry feedback suggests that improvements in water use and treatment efficiency are typically prioritized only when they also reduce energy use, carbon emissions, or costs. This study advocates for a direct two-way partnership between industry and research audiences to bring their attention toward sustainable industrial water use, treatment, and reuse.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Best practices for predictions of radionuclide activity concentrations and total absorbed dose rates to freshwater organisms exposed to uranium mining/milling

Predictions of radionuclide dose rates to freshwater organisms can be used to evaluate the radiological environmental impacts of releases from uranium mining and milling projects. These predictions help inform decisions on the implementation of mitigation measures. The objective of this study was to identify how dose rate modelling could be improved to reduce uncertainty in predictions to non-human biota. For this purpose, we modelled the activity concentrations of 210 Pb, 210 Po, 226 Ra, 230 Th, and 238 U downstream of uranium mines and mills in northern Saskatchewan, Canada, together with associated weighted absorbed dose rates for a freshwater food chain using measured activity concentrations in water and sediments. Differences in predictions of radionuclide activity concentrations occurred mainly from the different default partition coefficient and concentration ratio values from one model to another and including all or only some 238 U decay daughters in the dose rate assessments. Consequently, we recommend a standardized best-practice approach to calculate weighted absorbed dose rates to freshwater biota whether a facility is at the planning, operating or decommissioned stage. At the initial planning stage, the best-practice approach recommend using conservative site-specific baseline activity concentrations in water, sediments and organisms and predict conservative incremental activity concentrations in these media by selecting concentration ratios based on species similarity and similar water quality conditions to reduce the uncertainty in dose rate calculations. At the operating and decommissioned stages, the best-practice approach recommends relying on measured activity concentrations in water, sediment, fish tissue and wholebody of small organisms to further reduce uncertainty in dose rate estimates. This approach would allow for more realistic but still conservative dose assessments when evaluating impacts from uranium mining projects and making decision on adequate controls of releases.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Factors Influencing Propensity for Stress Relaxation Cracking in Inconel® Alloy 740H® and Practical Guidance for Applications

Inconel® alloy 740H® (UNS N07740) was the first age-hardenable nickel-based alloy approved by the ASME Boiler & Pressure Vessel Code for use in pressure-boundary applications. In recent years, advanced energy systems such as supercritical CO2 power cycles have utilized alloy 740H in large demonstration projects driven by the requirement for higher fluid temperatures and pressures. Stress relaxation cracking (SRxC) following post-weld heat-treatment (PWHT), also known as strain age cracking (SAC), has been identified in a limited number of weldments during these industrial builds resulting in focused research to further clarify factors influencing this cracking tendency. This paper will summarize some of the findings from shop and field fabrication leading to successful welds and characteristics of observed SRxC. Laboratory experiments supported by microstructural characterization will be presented to highlight the importance of variables such as strain, material starting condition, and PWHT temperatures. Finally, the results will be summarized within the context of practical guidance for industry to successfully weld the material in boiler, heat exchanger, and piping applications.

14 SOLAR ENERGY↗

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimizing high energy density sulfur cathodes: A multivariate approach to electrode formulation and processing

Lithium-sulfur (Li-S) batteries involve complex solid-liquid-solid phase transformations during both discharging and charging processes, where cathode materials, formulation, and structure play a crucial role. Here, a design of experiments (DoE) methodology and an empirical model are developed to systematically explore the interactions and trade-offs among cathode factors and process variables, and to obtain generalizable effects estimates for the multivariate system. Compared to the conventional one-factor-at-a-time (OFAT) approach, this work demonstrates advantages in both efficiency and accuracy by allowing the data to guide future research and decisions. Further, an optimized cathode formulation and processing parameters are predicted and validated experimentally, achieving over 1000 mAh g -1 in discharge capacity and improved cycling under practical lean electrolyte (4 µL mg -1 S) and high S-loading cathodes (>4 mg cm -2 ) conditions. The optimized cathode was scaled up and assembled into Li-S pouch cells, achieving 316 Wh kg -1 in cell-level energy, proving that the comprehensive and rigorous framework for optimizing complex systems with DoE leads to improved performance in a practical pouch cell system.

25 ENERGY STORAGE↗

Solving the Hele–Shaw flow using the Harrow–Hassidim–Lloyd algorithm on superconducting devices: A study of efficiency and challenges

The development of quantum processors for practical fluid flow problems is a promising yet distant goal. Recent advances in quantum linear solvers have highlighted their potential for classical fluid dynamics. In this study, we evaluate the Harrow–Hassidim–Lloyd (HHL) quantum linear systems algorithm (QLSA) for solving the idealized Hele–Shaw flow. Our focus is on the accuracy and computational cost of the HHL solver, which we find to be sensitive to the condition number, scaling exponentially with problem size. This emphasizes the need for preconditioning to enhance the practical use of QLSAs in fluid flow applications. Moreover, we perform shots-based simulations on quantum simulators and test the HHL solver on superconducting quantum devices, where noise, large circuit depths, and gate errors limit performance. Error suppression and mitigation techniques improve accuracy, suggesting that such fluid flow problems can benchmark noise mitigation efforts. Finally, our findings provide a foundation for future, more complex application of QLSAs in fluid flow simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Reliability Improvement and Effective Switching Layer Model of Thin-Film MoS 2 Memristors

2D memristors have demonstrated attractive resistive switching characteristics recently but also suffer from the reliability issue, which limits practical applications. Previous efforts on 2D memristors have primarily focused on exploring new material systems, while damage from the metallization step remains a practical concern for the reliability of 2D memristors. Here, the impact of metallization conditions and the thickness of MoS 2 films on the reliability and other device metrics of MoS 2 -based memristors is carefully studied. The statistical electrical measurements show that the reliability can be improved to 92% for yield and improved by ≈16× for average DC cycling endurance in the devices by reducing the top electrode (TE) deposition rate and increasing the thickness of MoS 2 films. Intriguing convergence of switching voltages and resistance ratio is revealed by the statistical analysis of experimental switching cycles. An “effective switching layer” model compatible with both monolayer and few-layer MoS 2 , is proposed to understand the reliability improvement related to the optimization of fabrication configuration and the convergence of switching metrics. In conclusion, the Monte Carlo simulations help illustrate the underlying physics of endurance failure associated with cluster formation and provide additional insight into endurance improvement with device fabrication optimization.

36 MATERIALS SCIENCE↗

A conservative, interface-resolved, compressible framework for the modeling and simulation of liquid/gas phase change

This paper presents a method for simulating evaporation in a compressible, interface-resolved framework appropriate for modeling problems of engineering interest. In order to achieve robustness and broad applicability, the method has been designed to discretely enforce consistent mass and thermal energy transport at the phase interface, to globally conserve mass, momentum, and energy, and to be capable of modeling compressible and incompressible systems. Verification is performed via the Sod-shock test, one-dimensional heat conduction, evaporation from a planar interface, and evaporation of three-dimensional droplets. Convergence with increasing mesh resolution is demonstrated in all tested configurations, and conservation is maintained near machine precision for a translating droplet. Conservation and accurate phase change rates are preserved at the low numerical resolutions commonly encountered in engineering calculations. Following verification, the method is validated by comparison to an empirical correlation for evaporating droplets in high temperature crossflow, and the presentation concludes with the simulation of an iso-octane spray at conditions representative of gasoline direct injection. In conclusion, successful verification, validation, and demonstrated practical utility suggest the method to be an accurate, efficient, and robust approach for the study of phase change in engineering systems.

97 MATHEMATICS AND COMPUTING↗

Understanding metal propagation in solid electrolytes due to mixed ionic-electronic conduction

Metal penetration into a solid electrolyte (SE) is one of the critical problems impeding the practical application of solid-state batteries. In this study, we investigate the conditions under which electronic conductivity of the SE can lead to metal deposition and fracture within the SE. Three different stages for void filling (metal plating initiation, metal growth, and metal compression) in the SE are identified. We show that a micron-size isolated void in the SE near the anode can be quickly filled in by metal and fractured when the developed pressure in the void grows larger than the maximum pressure the SE material can sustain. We find that the anode voltage and applied current density play a significant role in determining the vulnerability to metal deposition. We discuss several strategies to prevent electronic conductivity-driven metal propagation in electrolytes that are not fully dense, including the densified layers between the anode and SE.

25 ENERGY STORAGE↗

Electrochemical Cycling of Liquid Organic Hydrogen Carriers as a Sustainable Approach for Hydrogen Storage and Transportation

Hydrogen (H 2 ), as a high-energy-density molecule, offers a clean solution to carry energy. However, the high diffusivity and low volumetric density of H 2 pose a challenge for long-term storage and transportation. Liquid organic hydrogen carriers (LOHCs) have been suggested as a strategic way to store and transport hydrogen in stable molecules. More so, electrochemical LOHC cycling renders an opportunity to utilize renewable energy for hydrogen storage and transportation toward the goal of eliminating carbon emissions. In this Perspective, examples of electrochemical reactions of organic molecules and their suitability for LOHC couples are examined. A comparative carbon footprint assessment of electrochemical LOHC cycling processes against thermochemical and hybrid LOHC cycling processes was performed. The electrochemical LOHC cycling process had the lowest relative carbon footprint only when highly concentrated LOHCs were used as the feed or when purification of the LOHC product was not required. The carbon footprint in electrochemical cycling of diluted LOHC was primarily contributed to by the LOHC distillation separation process. A sensitivity analysis showed the carbon footprint LOHC concentration dependence during the electrochemical cycling process. Moreover, the electrolyte composition significantly affects the carbon footprint during electrochemical LOHC cycling. Energy utilization, water usage, and toxicity for electrochemical LOHC cycling are discussed to provide an overview for better economic and environmental practices. There are significant opportunities in the electrochemical cycling of LOHCs if appropriate conditions such as high concentrations of reactant, reversible redox cycling ability, high Faradaic efficiencies, and catalyst stabilities are achieved.

25 ENERGY STORAGE↗

Unveiling nano-scale crystal deformation using coherent X-ray dynamical diffraction

Visualization of internal deformation fields in crystalline materials helps bridge the gap between theoretical models and practical applications. Applying Bragg coherent diffraction imaging under X-ray dynamical diffraction conditions provides a promising approach to the longstanding challenge of investigating the deformation fields in micron-sized crystals. Here, we present an automatic differentiation-based reconstruction method that integrates dynamical scattering theory to accurately reconstruct deformation fields in large crystals. Using this forward model, our simulated and experimental results demonstrate that three-dimensional local strain information inside a large crystal can be accurately reconstructed under coherent X-ray dynamical diffraction conditions with Bragg coherent X-ray diffraction imaging. These findings open an avenue for extending the investigation of local deformation fields to microscale crystals while maintaining nanoscale resolution, leveraging the enhanced coherence and brightness of advanced X-ray sources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Possibilities of using practical limitations of an eavesdropper in quantum cryptography

An important advantage of quantum cryptography over classical cryptography consists in the fact that the security of the transmitted keys is not related to the assumptions about the eavesdropper capabilities and is guaranteed by the laws of nature. Nevertheless, in some situations it makes sense to consider some reasonable assumptions about the eavesdropper capabilities, which can increase the secret key distribution rate. Methods are proposed for legitimate users to employ some practical limitations, and attacks are constructed that the eavesdropper can apply under the conditions of these limitations. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

How Much Reserve Fuel: Quantifying the Maximal Energy Cost of System Disturbances

Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded disturbances, compared to a nominal, disturbance-free system. In particular, we consider the task of finite-time stabilization for a linear, time-invariant system. We compare the nominal energy required to achieve this task in the disturbance-free system to the worst-case energy over all feasible disturbances. Solving for the worst-case energy over all disturbances first leads to an optimal control problem with a least-squares solution, and then an infinite-dimensional optimization problem where we derive an upper bound on the solution. The comparison of energies is accomplished using additive and multiplicative metrics, for which we derive bounds. Simulation examples on an ADMIRE fighter jet model demonstrate the practicability of these metrics, and their variation with the distance of the initial condition from the origin and the task completion time.

koopman operator, resilience↗