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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability

We developed far-IR spectroscopic ellipsometer at the U4IR beamline of the National Synchrotron Light Source in Brookhaven National Laboratory. This ellipsometer is able to measure both, rotating analyzer and full-Mueller matrix spectra using rotating retarders, and wire-grid linear polarizers. We utilize exceptional brightness of synchrotron radiation in the broad spectral range between about 20 and 4000 cm{sup -1}. Fourier-transform infrared (FT-IR) spectrometer is used for multi-wavelength data acquisition. The sample stage has temperature variation between 4.2 and 450 K, wide range of {theta}-2{theta} angular rotation, {chi} tilt angle adjustment, and X-Y-Z translation. A LabVIEW-based software controls the motors, sample temperature, and FT-IR spectrometer and also allows to run fully automated experiments with pre-programmed measurement schedules. Data analysis is based on Berreman's 4 Multiplication-Sign 4 propagation matrix formalism to calculate the Mueller matrix parameters of anisotropic samples with magnetic permeability {mu}{ne} 1. A nonlinear regression of the rotating analyzer ellipsometry and/or Mueller matrix (MM) spectra, which are usually acquired at variable angles of incidence and sample crystallographic orientations, allows extraction of dielectric constant and magnetic permeability tensors for bulk and thin-film samples. Applications of this ellipsometer setup for multiferroic and ferrimagnetic materials with {mu}{ne} 1 are illustrated with experimental results and simulations for TbMnO{sub 3} and Dy{sub 3}Fe{sub 5}O{sub 12} single crystals. We demonstrate how magnetic and electric dipoles, such as magnons and phonons, can be distinguished from a single MM measurement without adducing any modeling arguments. The parameters of magnetoelectric components of electromagnon excitations are determined using MM spectra of TbMnO{sub 3}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Multilane Automated Driving With Optimal Control and Mixed-Integer Programming

Road vehicle lane changes often initiate traffic disturbances and can therefore impact road networks’ energy and time efficiency. Furthermore, unexpected changes in traffic conditions may also render lane changes counterproductive for the lane-changing vehicle. Vehicle-to-vehicle connectivity combined with anticipative control could address these challenges via improved lane change decisions by automated vehicles. In a move toward this objective, receding horizon control cast as a mixed-integer quadratic program is used to plan lane changing and acceleration in a coupled optimization. A long-term pacing module, based on Pontryagin’s minimum principle from optimal control theory, sets terminal and input references for receding horizon control to target a user’s expected travel time. To remove nonlinear vehicle dynamics from the receding horizon controller, lane change commands are passed to a pure pursuit steering module whose response is approximated by a second-order linear model. Here, comparison against a rule-based reactive algorithm in arterial and highway scenarios shows an 8.9%–13.7% reduction in energy consumption and a 5.2%–10.3% reduction in the travel time, along with navigational improvements.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2018

Biomimetic model-based advanced control strategy integrated with multi-agent optimization for nonlinear chemical processes

Here, a novel framework is proposed for integrating biomimetic-based advanced control and multi-agent optimization approaches for nonlinear chemical process applications. In particular, a Biologically-Inspired Optimal Control Strategy, denoted as BIO-CS, is combined with multi-agent optimization (MAO) techniques to provide optimal solutions for dynamic systems. In this combined framework, the BIO-CS algorithm employs gradient-based optimal control solvers for the intermediate problems associated with the leader-follower agents’ local interactions. Also, the MAO uses the capabilities of heuristic-based optimization techniques by sharing process information to obtain optimal operating setpoints for the controller considering an overall process objective. The applicability of the proposed method is demonstrated using a nonlinear, multivariable, process model of a fermentation system. Specifically, the optimal operating points are computed by the MAO implementation for setpoint tracking, trajectory tracking and plant-model mismatch scenarios for BIO-CS application. Results of the developed framework are compared to a gradient-based Sequential Quadratic Programming (SQP) technique and a classical proportional-integral (PI) controller in terms of optimization and control studies, respectively. As an additional contribution, BIO-CS is also cast as a model predictive controller (MPC) for the first time and compared to the agent-based BIO-CS approach in terms of computational time and tracking error. Closed-loop control results show up to 46% improvement in tracking performance during transient for the multi-agent BIO-CS when compared to BIO-CS as MPC for additional computational expense. The obtained results illustrate the capabilities of this novel integrated framework including BIO-CS as MPC to achieve desired nonlinear system performance for various scenarios.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations

While peak shaving is commonly used to reduce power costs, chemical process facilities that can reduce power consumption on demand during emergencies (e.g., extreme weather events) bring additional value through improved resilience. For process facilities to effectively negotiate demand response (DR) contracts and make investment decisions regarding flexibility, they need to quantify their additional value to the grid. We present a grid–centric mixed–integer stochastic programming framework to determine the value of DR for improving grid resilience in place of capital investments that can be cost prohibitive for system operators. We formulate problems using both a linear approximation and a nonlinear alternating current power flow model. Our numerical results with both models demonstrate that DR can be used to reduce the capital investment necessary for resilience, increasing the value that chemical process facilities bring through DR. Furthermore, the linearized model often underestimates the amount of DR needed in our case studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Quantum Chemical Calculations of the Spectroscopic Properties and Nonlinear Optical Activity of 2,6-Dibromo-3-Chloro-4-Fluoroaniline

The Fourier transform infrared (FT-IR) and Fourier transform Raman (FT-Raman) spectra of 2,6-dibromo-3-chloro-4-fluoroaniline in the solid phase were recorded and analyzed. Quantum chemical calculations of the optimized molecular structure, energies, nonlinear optical (NLO) analysis, molecular surfaces, and vibrational analysis of this substance were performed. The obtained results on the geometric structure and vibrational frequencies were compared with the observed data. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies also confirm that charge transfer occurs within the molecule. The detailed vibrational assignments were performed using the HF and DFT calculations, and the potential energy distribution (PED) was obtained by the vibrational energy distribution analysis (VEDA4) program. Finally, the effects of the amino, bromo, chloro, and fluoro substituents on the vibrational frequencies were investigated.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Supporting cost-effective watershed management strategies for Chesapeake Bay using a modeling and optimization framework

Extensive efforts to adaptively manage nutrient pollution rely on Chesapeake Bay Program’s (Phase 6) Watershed Model, called Chesapeake Assessment Scenario Tool (CAST), which helps decision-makers plan and track implementation of Best Management Practices (BMPs). We describe mathematical characteristics of CAST and develop a constrained nonlinear BMP-subset model, software, and visualization framework. This represents the first publicly available optimization framework for exploring least-cost strategies of pollutant load control for the United States’ largest estuary. The optimization identifies implementation options for a BMP subset modeled with load reduction effectiveness factors, and the web interface facilitates interactive exploration of >30,000 solutions organized by objective, nutrient control level, and for ~200 counties. We assess framework performance and demonstrate modeled cost improvements when comparing optimization-suggested proposals with proposals inspired by jurisdiction plans. Stakeholder feedback highlights the framework’s current utility for investigating cost-effective tradeoffs and its usefulness as a foundation for future analysis of restoration strategies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Coupled Multiphysics Simulations of Heat Pipe Microreactors Using DireWolf

DireWolf is a multiphysics software driver application designed to simulate heat pipe–cooled nuclear microreactors. Developed under the U.S. Department of Energy, Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the DireWolf software application’s objective is to provide the nuclear community with a design and safety analysis simulation capability. Based upon the NEAMS program Multiphysics Object-Oriented Simulation Environment (MOOSE) computational framework, DireWolf tightly couples nuclear microreactor physics, reactor physics, radiation transport, nuclear fuel performance, heat pipe thermal hydraulics, power generation, and structural mechanics to resolve the interdependent nonlinearities. DireWolf is capable of simulating both steady and transient normal reactor operation and several postulated failure scenarios. We will present the fundamental physics of heat pipe–cooled nuclear microreactors and the MOOSE-based software employed in DireWolf. Both steady and transient results for coupled reactor physics, radiation transport, and nuclear fuel performance are demonstrated.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Domain Aware Deep-learning Algorithms Integrated with Scientific-computing Technologies (DADAIST)

This technical report summarized the contribution of the DADAIST project funded by the Data Model Convergence Initiative via the Laboratory Directed Research and Development (LDRD) investments at Pacific Northwest National Laboratory (PNNL). Specifically, we report the development of the NeuroMANCER (Neural Modules with Adaptive Nonlinear Constraints and Efficient Regularizations), a new open-source Scientific Machine Learning library for formulating and solving parametric constrained optimization problems, physics-informed system identification, and parametric optimal control problems. NeuroMANCER is using differentiable programming to combine modern data-driven models and optimization modeling language into a coherent algorithmic and software framework. NeuroMANCER is a Pytorch-based framework and adopts much of its philosophy focused on research and development, rapid prototyping, and streamlined deployment. Strong emphasis is given to extensibility, interoperability with the PyTorch ecosystem, and quick adaptability to custom domain problems. Neuromancer repository contains a comprehensive library of differentiable modules, including custom activation functions, matrix factorizations, deep learning architectures, neural differential equations, differential equation solvers, implicit layers such as iterative solvers, high-level API for symbolic expressions, API for modeling and control of dynamical systems, and extensive set of tutorial code examples in the form of python scripts and jupyter notebooks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum Computing Strategy 2026

Quantum computing (QC) is a rapidly maturing technology with the potential for revolutionary impacts on stockpile stewardship science and national security. Recent developments in fault-tolerant architectures have compressed vendor roadmaps, and predictions of a production-ready quantum computer by the mid-2030s are becoming increasingly credible. This strategy provides a roadmap for integrating QC into the Advanced Simulation and Computing (ASC) program by investing in four strategic focus areas: 1. Develop Capabilities in Mission-Relevant Quantum Applications: ASC will prioritize developing quantum-ready applications in mission areas that have shown significant promise for quantum advantage, including simulations of materials in extreme environments, nuclear dynamics, solving linear and nonlinear partial differential equations, and uncertainty quantification. These applications directly support stockpile stewardship science and modernization objectives. 2. Conduct R&D in Algorithms, Software, and Hardware: Sustained research into quantum algorithms, robust software tools, and quantum hardware is essential. ASC will develop efficient quantum algorithms; invest in quantum compilers, debuggers, and performance tools; and explore specialized quantum hardware tailored to NNSA’s unique requirements. 3. Engage with Vendors and Partners: Early and active collaboration with commercial quantum hardware vendors and academic partners is critical. Through testbeds, co-design agreements, and quantum demonstration facilities, ASC will influence hardware design, gain early access to emerging technologies, and ensure that quantum platforms evolve to meet mission needs. 4. Build Knowledge, Experience, and Workforce: Expanding and upskilling the quantum-trained workforce is essential to long-term success. This includes hiring, internal training, university outreach, and postdoctoral support to ensure ASC maintains the expertise required to operate, program, and integrate quantum systems as they become available. While quantum computing will never replace classical computing, it has the potential to solve certain problems with speed and accuracy that would be unachievable using any conceivable classical high-performance computing (HPC) system. By investing strategically in QC, ASC will help propel the emergent QC industry, maintain U.S. technological leadership, ensure mission readiness, and position itself to rapidly adopt quantum technologies as they mature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Real-time control of connected vehicles in signalized corridors using pseudospectral convex optimization

Recent advances in Connected and Automated Vehicle (CAV) technologies have opened up new opportunities to enable safe, efficient, and sustainable transportation systems. However, developing reliable and rapid speed control algorithms in highly dynamic environments with complex inter-vehicle interactions and nonlinear vehicle dynamics is still a daunting task. In this paper, we develop a novel speed control method for CAVs to produce optimal speed profiles that minimize the fuel consumption and avoid idling at signalized intersections. To this end, an optimal control problem is formulated using the information of the upcoming traffic signal to adapt vehicles' speeds to avoid frequent stop-and-go driving patterns. Here, by applying the pseudospectral discretization method and the sequential convex programming method, the computational efficiency is greatly improved, enabling potential real-time on-vehicle applications. In addition, the algorithm is implemented under a model predictive control framework to ensure online control with instant response for collision avoidance and robust vehicle coordination. The proposed algorithm is verified through numerical simulations of three different traffic scenarios. The convergence and accuracy of the proposed approach are demonstrated by comparing with a popular nonlinear solver. Furthermore, the benefit of the proposed method in both traffic mobility and fuel efficiency is validated using the speed profile determined from a traffic following model in a simulation software as the baseline.

42 ENGINEERING↗
DOE OSTI2024

On the Impact of High-Order Harmonic Generation in Electrical Distribution Systems

The modern power grid has seen a rise in the integration of non-linear loads, presenting a significant concern for operators. These loads introduce unwanted harmonics, leading to potential issues such as overheating and improper functioning of circuit breakers. In pursuing a more sustainable grid, the adoption of electric vehicles (EVs) and photovoltaic (PV) systems in residential networks has increased. Understanding and examining the effects of high-order harmonic frequencies beyond $1.5$ kHz is crucial to understanding their impact on the operation and planning of electrical distribution systems under varying nonlinear loading conditions. This study investigates a diverse set of critical power electronic loads within a household modeled using PSCAD/EMTdc, analyzing their unique harmonic spectra. This information is utilized to run the time-series harmonic analysis program in OpenDSS on a modified IEEE 34 bus test system model. The impact of high-order harmonics is quantified using metrics that evaluate total harmonic distortion (THD), transformer harmonic-driven eddy current loss component, and propagation of harmonics from the source to the substation transformer.

Peerzada, Aaqib A. [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2018

Uncertainty quantification in ToxCast high throughput screening

High throughput screening (HTS) projects like the U.S. Environmental Protection Agency’s ToxCast program are required to address the large and rapidly increasing number of chemicals for which we have little to no toxicity measurements. Concentration-response parameters such as potency and efficacy are extracted from HTS data using nonlinear regression, and models and analyses built from these parameters are used to predict in vivo and in vitro toxicity of thousands of chemicals. How these predictions are impacted by uncertainties that stem from parameter estimation and propagated through the models and analyses has not been well explored. While data size and complexity makes uncertainty quantification computationally expensive for HTS datasets, continued advancements in computational resources have allowed these computational challenges to be met. This study uses nonparametric bootstrap resampling to calculate uncertainties in concentration-response parameters from a variety of HTS assays. Using the ToxCast estrogen receptor model for bioactivity as a case study, we highlight how these uncertainties can be propagated through models to quantify the uncertainty in model outputs. Uncertainty quantification in model outputs is used to identify potential false positives and false negatives and to determine the distribution of model values around semi-arbitrary activity cutoffs, increasing confidence in model predictions. At the individual chemical-assay level, curves with high variability are flagged for manual inspection or retesting, focusing subject-matter-expert time on results that need further input. This work improves the confidence of predictions made using HTS data, increasing the ability to use this data in risk assessment.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Fork Experiments in the Hot Cell Using Spent Fuel Rods for International Nuclear Safeguards

This work leveraged the rare availability of 25 full-length pressurized water reactor spent fuel rods and 1 irradiated mixed-oxide rod at an Oak Ridge National Laboratory hot cell. This was done to collect measurement data with two Fork detectors to assess the detectors’ capability of verifying operator declaration data and detecting partial defects in spent fuel, which are the two primary goals of international safeguards on spent nuclear fuel. The data can also be used to benchmark the ORIGEN module, which has been adopted in the International Atomic Energy Agency’s (IAEA’s)/European Atomic Energy Community’s (Euratom’s) Integrated Review and Analysis Program to predict the Fork detector count rates in real time. In this project, the authors first calibrated two Fork detectors—a standard one and a modified one—by using known strong neutron and gamma sources. Then, the authors measured all 26 fuel rods at multiple locations along the length. The fuel rods were then assembled into three arrays—2 × 2, 3 × 3, and 5 × 5—by using specially designed support grids to mimic fuel assemblies and measure the arrays with both detectors. For the 5 × 5 array, 4 and 8 fuel rods of the array were replaced in two separate cases with short stainless-steel rods to mimic two partial defect scenarios, and the arrays were measured before and after the replacements. Polyethylene blocks were used in this experiment to mimic water. The results show that the Fork detectors were able to verify operator declarations and detect partial defects in spent fuel, and the authors were the first to demonstrate this through experiments. A discovery was also made that determined the root cause of the nonlinear response to gamma dose in the ion chambers used in IAEA and Euratom’s Fork detectors. After the experiments, both detectors were retrieved from the hot cell for future use. The data collected in this project will be used in a parallel International Nuclear Safeguards Engagement Program (INSEP) project to enhance the safeguards in the Finnish spent fuel encapsulation plant, and the data will be useful to other projects in the future given the increased safeguards needs due to spent fuel transfer and disposal activities worldwide.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Advanced multiphysics coupling for LWR fuel performance analysis

Even the most basic nuclear fuel analysis is a multiphysics undertaking, as a credible simulation must consider at a minimum coupled heat conduction and mechanical deformation. The need for more realistic fuel modeling under a variety of conditions invariably leads to a desire to include coupling between a more complete set of the physical phenomena influencing fuel behavior, including neutronics, thermal hydraulics, and mechanisms occurring at lower length scales. This paper covers current efforts toward coupled multiphysics LWR fuel modeling in three main areas. The first area covered in this paper concerns thermomechanical coupling. The interaction of these two physics, particularly related to the feedback effect associated with heat transfer and mechanical contact at the fuel/clad gap, provides numerous computational challenges. An outline is provided of an effective approach used to manage the nonlinearities associated with an evolving gap in BISON, a nuclear fuel performance application. A second type of multiphysics coupling described here is that of coupling neutronics with thermomechanical LWR fuel performance. DeCART, a high-fidelity core analysis program based on the method of characteristics, has been coupled to BISON. DeCART provides sub-pin level resolution of the multigroup neutron flux, with resonance treatment, during a depletion or a fast transient simulation. Two-way coupling between these codes was achieved by mapping fission rate density and fast neutron flux fields from DeCART to BISON and the temperature field from BISON to DeCART while employing a Picard iterative algorithm. Finally, the need for multiscale coupling is considered. Fission gas production and evolution significantly impact fuel performance by causing swelling, a reduction in the thermal conductivity, and fission gas release. The mechanisms involved occur at the atomistic and grain scale and are therefore not the domain of a fuel performance code. However, it is possible to use lower length scale models such as those used in the mesoscale MARMOT code to compute average properties, e.g. swelling or thermal conductivity. These may then be used by an engineering-scale model. Examples of this type of multiscale, multiphysics modeling are shown.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Coiling free electron matter waves

Here we demonstrate particle beams that spiral in free space devoid of external fields. The beams consist of electrons in two lobes that twist around each other along the optical axis, such that each electron can be described by a two-lobed probability distribution that rotates as it propagates. Furthermore, we demonstrate that this twisting distribution can undergo programmed periods of angular acceleration. These unusual states are produced by preparing each free electron wavefunction in a superposition of non-diffracting Bessel modes that carry orbital angular momentum using nanofabricated diffraction holograms. The holograms can encode nonlinear azimuthal phase so that the resulting electron probability distribution twists in space in a controllable manner, accelerating and decelerating during propagation, without any radiation. This work provides a new platform to explore the dynamics of electrons in magnetic fields, and opens the possibility of producing other types of particle beams with coiling geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

FAST INJECTION SYSTEM R&D FOR THE APS UPGRADE

The MBA upgrade for the APS will operate with bunch swap out and on axis injection. The planned 324 bunch fill pattern places difficult demands on the injection and extraction kickers. The present concept uses dual stripline kickers driven by high Voltage pulsers. Minimizing perturbation on adjacent bunches requires very fast rise and fall times with relatively narrow ~20 nsec, 15 kV pulses. To achieve these requirements we have initiated a multifaceted R&D program. The R&D includes the HV pulser, stripline kicker and HV feedthrough. We have purchased a commercial dual channel HV pulser and are evaluating its performance and reliability. In addition, we are investigating the feasibility of using nonlinear ferrite loaded coaxial cables (shockwave transmission line) to sharpen the leading and trailing edges of high voltage pulses. We are also developing a prototype kicker and high voltage feedthrough. The requirements for injection and extraction, progress on prototype development and results of our HV pulser investigations will be reported.

Lenkszus, F.↗
DOE OSTI2014

Final Report - Interaction of radiation and charged particles in miniature plasma structures

The extension of our program to the development of theories and models capable of describing the interactions of intense laser pulses and charged particles in miniature plasma channels is reported. These channels, which have recently been created in the laboratory, have unique dispersion properties that make them interesting for a variety of applications including particle acceleration, high harmonic generation, and THz generation. Our program systematically explored the properties of these channels, including dispersion, losses, and coupling. A particular application that was pursued is the generation of intense pulses of THz radiation by short laser pulses propagating these channels. We also explored the nonlinear dynamics of laser pulses propagating in these channels.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗