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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Use of Physics Based Management Optimization for Groundwater Remedy Design - 18671

Numerical modeling coupled with formal mathematical optimization techniques was used to design a groundwater remedy strategy to address a carbon tetrachloride (CCl{sub 4}) plume covering several square miles. The optimization approach, methodology, and project costs are described. The site consists of a large grain elevator in Nebraska. CCl{sub 4} was used as a fumigant and subsequently impacted soils and groundwater. Remedy design focused on the more diffuse plume, which extended approximately 4.5 miles down gradient of the source area. An eleven-layer model was developed and calibrated to observed groundwater conditions. This model was linked with formal optimization techniques to identify the best design capable of meeting client specified requirements and well location limitations. The planned system included requirements on the location of extraction and injection wells, total system flow rate, number of management periods, and specific constraints limiting further plume expansion. A separate trinitrotoluene (TNT) contaminant plume from a third party was located vertically above the leading edge of the CCl{sub 4} plume within the same aquifer. A further constraint imposed was that the design could not affect or cause additional migration of the TNT plume. Optimal system design was determined using HydroGeoLogic's Physics Based Management Optimization (PBMO{sup TM}) system. Over 38,000 candidate solutions consisting of different combinations of pumping and injection wells locations and rates, were evaluated through flow modeling coupled with either particle tracking or fully convective-dispersive transport simulations to determine the optimal design. Planning for installation of the optimal design is underway. Simulations were completed on a distributed computing platform consisting of 3 Quad Core PCs. Flow and particle tracking simulations required less than 2 minutes per simulation. Coupled flow and transport simulation run times were generally between 30-40 minutes per simulation. The total costs for developing the groundwater flow model and completing the subsequent optimal design were approximately $400,000. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

Development of Thermoacoustic Sensors for Sodium-cooled Fast Reactors

This Final Report refers to the project “Development of Thermoacoustic Sensors for Sodium-cooled Fast Reactor Systems”, which was led by Westinghouse Electric Company (Westinghouse) and carried out in collaboration with Argonne National Laboratory (ANL) and University of Pittsburgh. Thermo-acoustic Power Sensors (TAPS) are self-powered, wireless sensors envisioned for measuring key parameters, such as local temperature and neutron flux, in a nuclear reactor core. This project was intended to specifically investigate their applicability to Sodium-cooled Fast Reactors (SFR). TAPS are non-invasive (wireless) and passive (self-powered) devices. The passivity derives from their ability to use conditions that “naturally” exist in a nuclear reactor, such as gamma and neutron flux, as power sources. They generate oscillating pressure waves (i.e., sound waves) which, with a frequency and amplitude dependent upon these conditions, can travel through the core and associated structures, and reach the outside of the reactor vessel where a properly designed network of receivers can detect and interpret them. These receivers require a very small amount of power which, during loss of power events, can be provided for example by harvesting gamma radiation energy, thus resulting in a monitoring system that can function both during normal operation and during loss of power events. The project aimed at TAPS development through a series of tasks which are listed and briefly discussed as follows. TASK 1 – Sensor hardware design Subtask 1a: Assessment of sensor applications to SFRs Subtask 1b: Development of sensor functional requirements Subtask 1c: Definition of sensor hardware design specifications Task description: TAPS design was informed by considerations on their application (Subtask 1a), both the ultimate one in an SFR and the actual one in the ANL testing facilities that was intended to be used in support of the project. Considerations were made to identify optimum sensor design features that optimize the sensor size, materials, and output signal, for installation inside an SFR core. These considerations led to the development of Functional Requirements (Subtask 1b) and Design Requirements (Subtask 1c). TASK 2 – Sensor Hardware Manufacture Subtask 2a: Sensor hardware construction drawing development Subtask 2b: Sensor manufacture and assembly Task description: TAPS technical drawings were developed (Subtask 2a) using the Design Requirements established under Task 1. Subsequently, in spite of some problems which ultimately caused the program to be delayed, TAPS manufacturing was completed based on drawings (Subtask 2b). TASK 3 – Development of TAPS Signal Measurement System and TAPS Testing in Water Subtask 3a: Design, assembly and testing of signal measurement system, and TAPS testing in water Subtask 3b: Signal prediction-correction methodology development Task description: An assessment was performed on the techniques that can potentially be used to detect the signals emitted by the TAPS, e.g. a fiber-optic based acoustic signal measurement system, a laser vibrometer system, or an accelerometer-based system. The most suited technology, i.e. the accelerometer-based system, was developed further, and tested in water (Subtask 3a). Moreover, efforts were made to develop the methodology required to determine the actual system temperature and neutron flux distribution using differences between the measured and predicted TAPS responses (Subtask 3b). TASK 4 – Sensor System Testing in Sodium Subtask 4a: Test plan development Subtask 4b: Design, assembly and testing in small-scale sodium facility Subtask 4c: Design, assembly and testing in large-scale sodium and structures facility Task description: Upon proper test plan development (Subtask 4a), the fabricated TAPS was planned to be tested in sodium, by using two sodium facilities at ANL having different size and different purpose. The Under Sodium Viewing (USV) small-scale facility was intended to be used to investigate the effect of sodium on the sensor and its performance (Subtask 4b). The Mechanism Engineering Test Loop (METL) large-scale facility was instead intended to be used to assess the additional effect of prototypical SFR structures, such as fuel assembly mockup or parts of the core restrain structure, on sensor performance (Subtask 4c). As discussed in Section 3.2.2.7, unexpected issues during the TAPS manufacturing process resulted in some activities being delayed, with the TAPS and USV facility developed to the point to be ready for testing in sodium, however without the possibility to actually perform such testing (including the testing in METL) due to the end of the program’s performance period. Overall, through the development and testing (in water only) of two TAPS devices (a First-Generation TAPS followed by an optimized Second-Generation TAPS), the project confirmed the capability of this technology to generate acoustic signals proportional to temperature, which can be detected through a network of accelerometers identified as the best-suited type of receivers for acoustic signal detection. Moreover, the project also developed a computational model to predict the characteristics of the acoustic signals being generated, which combines thermal analysis of the TAPS with Finite Element Modeling (FEM)-aided acoustic characterization of the system. This model was benchmarked against experimental data collected during the project and, although general agreement was obtained, some limitations of the modeling methods were identified, which require additional development. Additional testing is needed in order to assess the effect, on TAPS operation and performance, of environmental changes resulting from the transition from water to liquid sodium. Such testing, which is suggested to be performed in the future, should look specifically at 1) both the effect resulting from the different thermoacoustic behavior of sodium (relative to water) and the effects of higher temperature on TAPS performance, and 2) the performance of the sensor-receiver system when multiple TAPS are used simultaneously and prototypical reactor structures are positioned in the testing environment. The latter testing is needed to assess the effects that potential signal attenuation/ distortion phenomena, as well as potential interference between signals emitted simultaneously, have on the performance of the technology for ultimate application in a nuclear reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Optimization of Allosteric With-No-Lysine (WNK) Kinase Inhibitors and Efficacy in Rodent Hypertension Models

The observed structure–activity relationship of three distinct ATP noncompetitive With-No-Lysine (WNK) kinase inhibitor series, together with a crystal structure of a previously disclosed allosteric inhibitor bound to WNK1, led to an overlay hypothesis defining core and side-chain relationships across the different series. Furthermore, this in turn enabled an efficient optimization through scaffold morphing, resulting in compounds with a good balance of selectivity, cellular potency, and pharmacokinetic profile, which were suitable for in vivo proof-of-concept studies. When dosed orally, the optimized compound reduced blood pressure in mice overexpressing human WNK1, and induced diuresis, natriuresis and kaliuresis in spontaneously hypertensive rats (SHR), confirming that this mechanism of inhibition of WNK kinase activity is effective at regulating cardiovascular homeostasis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Volcano‐like Activity Trends in Au@Pd Catalysts: The Role of Pd Loading and Nanoparticle Size

The addition of palladium (Pd) to preformed gold nanoparticles (Au NPs) enables the formation of core‐shell structures with enhanced catalytic performance in oxidation reactions. However, predicting the precise palladium content required to achieve maximum catalytic activity remains difficult based on current understanding. Herein, Pd was systematically introduced onto titania‐supported Au NPs (2, 6, and 10 nm) to evaluate their performance in benzyl alcohol oxidation. A volcano‐like trend in catalytic activity was observed, where activity increased with Pd addition, peaked, and then declined. The Pd loading required for maximum activity depended on Au NP size: ≈40 at% Pd/Au for 2.6 nm, ≈20 at% Pd/Au for 6.4 nm, and ≈12.5 at% Pd/Au for 10.6 nm. For Au NPs > 6 nm, peak activity aligned with monolayer Pd coverage, while for smaller NPs (2–3 nm), optimal Pd content was below monolayer predictions. X‐ray absorption spectroscopy revealed a core‐shell structure at low Pd content, but higher Pd loadings led to Pd diffusion into the Au core. This structural transformation likely caused activity decline, indicating that AuPd alloying negatively impacts catalysis. These results highlight that core‐shell Au@Pd catalysts outperform AuPd alloys and provide crucial insights for designing highly active bimetallic catalysts.

X-ray absorption spectroscopy↗
DOE OSTI2017

Cache Locality Optimization for Recursive Programs

We present an approach to optimize the cache locality for recursive programs by dynamically splicing--recursively interleaving--the execution of distinct function invocations. By utilizing data effect annotations, we identify concurrency and data reuse opportunities across function invocations and interleave them to reduce reuse distance. We present algorithms that efficiently track effects in recursive programs, detect interference and dependencies, and interleave execution of function invocations using user-level (non-kernel) lightweight threads. To enable multi-core execution, a program is parallelized using a nested fork/join programming model. Our cache optimization strategy is designed to work in the context of a random work stealing scheduler. We present an implementation using the MIT Cilk framework that demonstrates significant improvements in sequential and parallel performance, competitive with a state-of-the-art compile-time optimizer for loop programs and a domain- specific optimizer for stencil programs.

Lifflander, Jonathan↗
DOE OSTI2020

Rapid generation of optimal generalized Monkhorst-Pack grids

In this report computational modeling of the properties of crystalline materials has become an increasingly important aspect of materials research, consuming hundreds of millions of CPU-hours at scientific computing centers around the world each year, if not more. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. We have previously demonstrated that performing such integrals using generalized Monkhorst-Pack k-point grids can roughly double the speed of these calculations relative to the widely-used traditional Monkhorst-Pack grids. However the generation of optimal generalized Monkhorst-Pack grids is not implemented in most software packages due to the computational cost and difficulty of identifying the best grids. To address this problem, we present new algorithms that allow rapid generation of optimal generalized Monkhorst-Pack grids on the fly. We demonstrate that the grids generated by these algorithms are on average significantly more efficient than those generated using existing algorithms across a range of grid densities. For grids that correspond to a real-space supercell with at least 50 Å between lattice points, which is sufficient to converge density functional theory calculations within 1 meV/atom for nearly all materials, our algorithm finds optimized grids in an average of 0.19 s on a single processing core. To facilitate the widespread adoption of this approach, we present new open-source tools including a library designed for integration with third-party software packages.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Surface and Interface Control in Nanoparticle Catalysis

The surface and interfaces of heterogeneous catalysts are essential to their performance as they are often considered to be active sites for catalytic reactions. With the development of nanoscience, the ability to tune surface and interface of nanostructures has provided a versatile tool for the development and optimization of a heterogeneous catalyst. In this Review, we present the surface and interface control of nanoparticle catalysts in the context of oxygen reduction reaction (ORR), electrochemical CO 2 reduction reaction (CO 2 RR), and tandem catalysis in three sections. In the first section, we start with the activity of ORR on the nanoscale surface and then focus on the approaches to optimize the performance of Pt-based catalyst including using alloying, core-shell structure, and high surface area open structures. In the section of CO 2 RR, where the surface composition of the catalysts plays a dominant role, we cover its reaction fundamentals and the performance of different nanosized metal catalysts. Finally, for tandem catalysis, where adjacent catalytic interfaces in a single nanostructure catalyze sequential reactions, we describe its concept and principle, catalyst synthesis methodology, and application in different reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Parameterizing empirical interatomic potentials for predicting thermophysical properties via an irreducible derivative approach: the case of ThO 2 and UO 2

The accuracy of classical physical property predictions using molecular dynamics simulations is determined by the quality of the interatomic potentials. Here we introduce a training approach for empirical interatomic potentials (EIPs) which is well suited for capturing phonons and phonon-related properties. Our approach is based on direct comparisons of the second- and third-order irreducible derivatives (IDs) between an EIP and the Born–Oppenheimer potential within density functional theory (DFT) calculations. IDs fully exploit space group symmetry and allow for training without redundant information. We demonstrate the fidelity of our approach in the context of ThO 2 and UO 2 , where we optimize parameters of an embedded-atom method potential in addition to core–shell interactions. Our EIPs provide thermophysical properties in good agreement with DFT and outperform widely utilized EIPs for phonon dispersion and thermal conductivity predictions. Reasonable estimates of thermal expansion and formation energies of Frenkel pairs are also obtained.

empirical interatomic potential↗
DOE OSTI2017

Alternative difference analysis scheme combining R -space EXAFS fit with global optimization XANES fit for X-ray transient absorption spectroscopy

Time-resolved X-ray absorption spectroscopy (TR-XAS), based on the laser-pump/X-ray-probe method, is powerful in capturing the change of the geometrical and electronic structure of the absorbing atom upon excitation. TR-XAS data analysis is generally performed on the laser-on minus laser-off difference spectrum. Here, a new analysis scheme is presented for the TR-XAS difference fitting in both the extended X-ray absorption fine-structure (EXAFS) and the X-ray absorption near-edge structure (XANES) regions. R -space EXAFS difference fitting could quickly provide the main quantitative structure change of the first shell. The XANES fitting part introduces a global non-derivative optimization algorithm and optimizes the local structure change in a flexible way where both the core XAS calculation package and the search method in the fitting shell are changeable. The scheme was applied to the TR-XAS difference analysis of Fe(phen) 3 spin crossover complex and yielded reliable distance change and excitation population.

Zhan, Fei↗
DOE OSTI2018

Real-Time Simulation of Modular Multilevel Converters

Modular multilevel converters (MMCs) are one of the most popular configurations of voltage-source converters (VSCs) used in applications like high-voltage direct current (HVdc) transmission systems and flexible alternate current transmission systems (FACTS). They have a large number of modules with thousands of capacitors and semiconductor devices, which make it hard to simulate in real-time. In this paper, a low-cost high-performance computing (HPC) configuration to simulate MMCs in real-time is proposed. The configuration uses a HPC digital signal processor (DSP) with 8 cores. An advanced MMC simulation algorithm is implemented using HPC techniques to optimize the real-time performance in the DSP. A comparison is performed with existing solutions to show the superiority of the proposed configuration and algorithms.

Debnath, Suman↗
DOE OSTI2021

Flux Switching Permanent Magnet Motor with Metal Amorphous Nanocomposite Soft Magnetic Material and Rare Earth Free Permanent Magnets

The power losses in high power-density motors due to high rotational speed and/or high pole counts may be reduced adopting metal amorphous nanocomposites (MANCs) featuring low power loss and a relatively high flux density (~1.3 T). We recently proposed a flux switching permanent magnet (FSPM) motor with a rating of 2.5 kW at 1400 Hz electrical speed by incorporating low loss (< 3 W/kg at 1 kHz) FeNi-based MANC material with projected iron loss of about 5 W. The motor design allows use of rare earth-free permanent magnets. For incorporation of MANC materials, an axial flux motor where the rotor and stator core are made from a wound ribbon core has been developed. We have performed a 3-d FEA to optimize the design and built and tested a prototype demonstrating that the low loss MANC material can be used for motor applications.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Automated Operational Forecasting of Monsoon Low Pressure Systems

Monsoon low pressure systems (LPSs) are the dominant rain-bearing weather system of South Asia, often producing extreme precipitation and hydrological disasters in a region inhabited by nearly two billion people. Despite the importance of these storms, no operational system has automatically identified and tracked LPS in real time in numerical weather prediction model output; many commonly used vortex-tracking algorithms are ill suited for monsoon LPS because of the weak winds and cold cores of these systems. Here, we describe a new system that uses optimized algorithms to identify monsoon LPS in short- to medium-range forecasts from the U.S. Global Ensemble Forecast System (GEFS) and a version of the deterministic Global Forecast System (GFS) adapted and used operationally by the Indian Institute of Tropical Meteorology (IITM). We also assess the historical performance of these models in forecasting South Asian monsoon LPS, comparing this with the performance of the Integrated Forecasting System of the ECMWF. We assess the accuracy of model predictions of LPS genesis, position, intensity, and precipitation rates for forecast lead times of 1–5 days, yielding quantitative information on model biases to guide operational forecasters and disaster managers. The system we introduce here could be extended to other low-latitude regions affected by dynamically weak, heavily precipitating atmospheric vortices that are often not included in tropical cyclone inventories.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

DARPA TRADES Annual Report.

During calendar year 2017, Sandia National Laboratories (SNL) made strides towards developing an open portable design platform rich in highperformance computing (HPC) enabled modeling, analysis and synthesis tools. The main focus was to lay the foundations of the core interfaces that will enable plug-n-play insertion of synthesis optimization technologies in the areas of modeling, analysis and synthesis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Hydrogen Diffusivity Measurements of YH 1.87 Moderator Material with Incoherent Quasielastic Neutron Scattering

Yttrium hydride is an optimal choice of moderator material for thermal neutron spectrum reactors requiring small core volumes. The Transformation Challenge Reactor (TCR) program at Oak Ridge National Laboratory (ORNL) aims to develop an additively manufactured microreactor core by leveraging recent advances in materials, manufacturing, data analytics, and high-fidelity modeling and simulation. Yttrium hydride was selected as the moderator material for TCR due to its high moderating power, which enables the spatially efficient reactor design and thermal stability that is superior when compared with zirconium hydride. Hydrogen desorption from yttrium hydride is expected at elevated temperatures, posing safety and performance concerns. As a lifetime component in advanced reactors, appropriate strategies to mitigate hydrogen release from yttrium hydride over long-term reactor operation are required. Understanding hydrogen mobility in yttrium hydride provides the scientific basis for developing a hydrogen barrier for hydride moderator and predicting the hydrogen redistribution within the material during various operational conditions. This study investigated the hydrogen motion in YH 1.87 as a function of temperature ranging from 200 to 1,173 K using incoherent quasielastic neutron scattering (IQNS) at the Spallation Neutron Source (SNS). The results are presented and discussed in terms of hydrogen self-diffusion coefficients, activation energy for translational hydrogen motion, and hydrogen jump distances. Based on the IQNS data, YH 1.87 is found to be stable at high temperatures with no translational H motion below 1,023 K within the IQNS detection limits. In the temperature range of 1,073–1,173 K, hydrogen diffusivity in YH 1.87 is $D = 4.57 X 10^{⁻3} [m^2/s] exp (⁻\frac{1.73[eV]}{RT}$). The hydrogen concentration’s dependence on hydrogen diffusivity is also discussed in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Exponential acceleration of macroscopic quantum tunneling in a Floquet Ising model

The exponential suppression of macroscopic quantum tunneling (MQT) in the number of elements to be reconfigured is an essential element of broken symmetry phases. This suppression is also a core bottleneck in quantum algorithms, such as traversing an energy landscape in optimization, and adiabatic state preparation more generally. In this work, we demonstrate exponential acceleration of MQT through Floquet engineering with the application of a uniform, high frequency transverse drive field. Using the ferromagnetic phase of the transverse field Ising model in one and two dimensions as a prototypical example, we identify three phenomenological regimes as a function of drive strength. For weak drives, the system exhibits exponentially decaying tunneling rates but robust magnetic order; in the crossover regime at intermediate drive strength, we find polynomial decay of tunnelling alongside vanishing magnetic order; and at very strong drive strengths both the Rabi frequency and time-averaged magnetic order are approximately constant with increasing system size. We support these claims with extensive full wavefunction and tensor network numerical simulations, and theoretical analysis. An experimental test of these results presents a technologically important and novel scientific question accessible on NISQ-era quantum computers.

Grattan, George↗
DOE OSTI2018

New generation of effective core potentials from correlated calculations: 2nd row elements

Very recently, we have introduced correlation consistent effective core potentials (ccECPs) derived from many-body approaches with the main target being its use in explicitly correlated methods but also in mainstream approaches. The ccECPs are based on reproducing excitation energies for a subset of valence states, i.e., achieving a near-isospectrality between the original and pseudo Hamiltonians. Additionally, binding curves of dimer molecules have been used for refinement and overall improvement of transferability over a range of bond lengths. Here we apply similar ideas to the second row elements and study several aspects of the constructions in order to find the optimal (or nearly-optimal) solutions within the chosen ECP forms with 3s, 3p valence space (Ne-core). New constructions exhibit accurate low-lying atomic excitations and equilibrium molecular bonds (on average within ≈ 0.03 eV and 3 mA), however, the errors for A1 and Si oxide molecules at short bond lengths are notably larger for both ours and existing ECPs. Assuming this limitation, our ccECPs show a systematic balance between the criteria of atomic spectra accuracy and transferability for molecular bonds. Finally, in order to provide another option with much higher uniform accuracy, we also construct He-core ECPs for the whole row with typical discrepancies of ≈ 0.01 eV or smaller.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Temperature-Dependent Evolution of the Oxidation States of Cobalt and Platinum in Co 1– x Pt x Clusters under H 2 and CO + H 2 Atmospheres

Co1-xPtx clusters of 2.9-nm size with a range of atomically precise Pt/Co atomic ratios (x = 0, 0.25, 0.5, 0.75, 1) were synthesized using the mass-selected low-energy cluster beam deposition (LECBD) technique and soft-landed onto an amorphous alumina thin film prepared by atomic layer deposition (ALD). Utilizing ex situ X-ray photoemission spectroscopy (XPS), the oxidation state of the as-made clusters supported on Al2O3 was determined after both a 1-h-long exposure to air and aging for several weeks while exposed to air. Next, the aged duster samples were characterized by grazing-incidence X-ray absorption spectroscopy (GIXAS) and then pretreated with diluted hydrogen and further exposed to the mixture of diluted CO and H-2 up to 225 degrees C at atmospheric pressure, and the temperature-dependent evolutions of the particle size/shape and the oxidation states of the individual metal components within the dusters were monitored using in situ grazing-incidence small-angle X-ray scattering and X-ray absorption spectroscopy (GISAXS/GIXAS). The changes in the oxidation states of Co and Pt exhibited a nonlinear dependence on the Pt/Co atomic ratio of the dusters. For example, a low Pt/Co ratio (x <= 0.5) facilitates the formation of Co(OH)(2), whereas a high Pt/Co ratio (x = 0.75) stabilizes the Co3O4 composition instead through the formation of a Co-Pt core-shell structure where the platinum shell inhibits the reduction of cobalt in the core of the Co1-xPtx alloy dusters. The obtained results indicate methods for optimizing the composition and structure of binary alloy clusters for catalysis.

Yang, Bing↗
DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗