Results for “Algorithms and theoretical developments” — Page 33

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↗

DOE OSTI2026

Reconstruction of atmospheric neutrinos in DUNE’s horizontal-drift far-detector module

This paper reports on the capabilities in reconstructing and identifying atmospheric neutrino interactions in one of the Deep Underground Neutrino Experiment’s (DUNE) far detector modules, a liquid argon time projection chamber (LArTPC) with horizontal drift (FD-HD) of ionization electrons. The reconstruction is based upon the workflow developed for DUNE’s long-baseline oscillation analysis, with some necessary machine-learning models’ retraining and the addition of features relevant only to atmospheric neutrinos such as the neutrino direction reconstruction. Where relevant, the impact of the detection of the charged particles of the hadronic system is emphasized, and comparisons are carried out between the case when lepton-only information is considered in the reconstruction (as is the case for many neutrino oscillation experiments), versus when all particles identified in the LArTPC were included. Three neutrino direction reconstruction methods have been developed and studied for the atmospheric analyses: using lepton-only information, using all reconstructed particles, and using only correlations from reconstructed hits. The results indicate that incorporating more than just lepton information significantly improves the resolution of both neutrino direction and energy reconstruction. The angle reconstruction algorithms developed in this work result in no strong dependence on particle direction for reconstruction efficiencies or neutrino flavor identification. This comprehensive review of the reconstruction of atmospheric neutrinos in DUNE’s FD-HD LArTPC is the first step towards developing a first neutrino oscillation sensitivity analysis, which will ready DUNE for its first measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRSDate not supplied

Development of a Ground Multi-Mission Low-Cost Optical Terminal (LCOT) for Free-Space Optical Communications

Once confined to the realm of laboratory experiments and theoretical papers, space-based laser communications (lasercomm) are on the verge of achieving mainstream status. Organizations from Facebook to NASA, and missions from cubesats to Orion are employing lasercomm to achieve gigabit communication speeds at mass and power requirements lower than that of traditional radio frequency (RF) methods. Since first demonstrating free-space optical communications services with Lunar Laser Communications Demonstration (LLCD) in 2013, NASA has invested in developing optical communications technologies and capabilities to enhancing its space communications networks. Along with evolving optical space terminals, NASA is also developing lasercomm grounds stations capable of meeting the rapidly increasing data volume demands of upcoming missions, from low-earth to lunar orbits and beyond and integrating these advanced capabilities into its Near-Space and Deep Space Networks. To meet this emerging need, the Low-Cost Optical Terminal (LCOT) project at NASA’s Goddard Space Flight Center (GSFC) is designing, building and validating a prototype for a flexible, multi-mission, and economical optical ground terminal that could be used as a blueprint for a global network of optical ground stations, capable of supporting a wide variety of missions. To date a major impediment to widespread adoption of laser communication has been the lack of an existing ground network infrastructure. A mission that wishes to take advantage of laser communication not only needs to invest in an optical space terminal, but it must also finance the creation of ground terminals to receive the downlink signal. This adds significant additional cost. Missions that do decide to incur the cost of financing a network of ground terminals end up building highly specialized optical receivers that are operable as receivers for that specific mission only. Significant Non-Recurring Engineering (NRE) cost is invested to build highly specialized one-of-a-kind ground terminals that go into storage after that particular mission is over. This is not an economical approach and does nothing to grow the number of optical ground stations available to future missions. In essence each mission that wants to take advantage of the benefits of lasercom has to start from scratch to provide a ground terminal network to support it. As long as this is the case, the cost for using laser communications will be too high for most missions to consider. LCOT intends to close this gap in technology by designing and developing a standard optical ground terminal design that is flexible enough to serve as a receiver for a wide range of future missions – a ground terminal that can be quickly reconfigured to receive downlinks at different wavelengths using different signal formats. Not only does LCOT have the industry-building objectives of utilizing commercial-off-the-shelf (COTS) components to the maximum extent possible, but also spurs the commercial development of other necessary lasercomm components not currently offered by industry. Finally, LCOT will give NASA scientists and engineers a facility where they can gain real-world experience with optical communications. It will give engineers a cost-effective way to try out new concepts and processes by providing the infrastructure for such testing. In this way it is hoped LCOT will serve as a stimulus for innovation in optical communications and speed its widespread adoption by future missions. The LCOT is comprised of five subsystems: Free-Space Optical, Transceiver, Amplifier, Monitor and Control, and Observatory Infrastructure. In August 2021, the LCOT team installed a 70 cm telescope, developed by Planewave Instruments that was optimized for optical communications. Free-Space Optical subsystem comprises of the telescope and its associated hardware, including a transmitter optical assembly, wide field cameras, two optical benches, and an adaptive optics subsystem. The transmit optical assembly, a unique concept design, is a cluster of four functionally independent transmit subassemblies located on the receive telescope. In addition to receiving optical signals and directing the expanded beam with high precision to the space terminal, it also performs tracking functions. The transmit optical assembly will support operations from Low Earth Orbit (LEO) through lunar and will be used as a template for industry manufacturing. The Optical Infrastructure subsystem is responsible for providing environmentally controlled shelters for LCOT equipment and various other systems. To maintain the safety and proper functionality of the telescope, a 16 ft Astrohaven clamshell dome procured which provides all-sky coverage without the need to rotate the dome. Additionally, Atmospheric Monitoring Assembly (AMA) will be part of optical infrastructure subsystem to ensure accurate performance of the LCOT. Like existing optical ground stations, LCOT will measure standard weather station parameters, infrared all sky image of cloud cover, and cloud height. LCOT, however, adds requirements for measuring night time seeing and, in the future, daytime seeing. Unlike other optical ground terminals, the LCOT is transceiver agnostic; user transceivers may be duplex transceivers, standalone receivers, or standalone transmitters with or without acquisition beacon functionality. As such, the LCOT project accommodates testing with external customer transceivers in a flexible manor, further complimenting its intended multi-mission goals. Another unique component of LCOT is the use of a new amplifier technology – the Very Large Mode Area (VLMA) amplifiers. This new technology allows LCOT to avoid the issues faced by previous laser communications ground terminals, gives users more flexibility and modular capability, and is capable of reaching an order of magnitude higher peak power than traditional High Power Optical Amplifiers (HPOA). One drawback of the VLMA HPOA approach is that the amplified light is output into free-space. The solution developed by LCOT is an optics train that couples the output of the VLMA amplifier into a short fiber for transport to the transmit telescopes with high efficiency. Like many of the LCOT components, a set of detailed manufacturing drawings have been created for the optics train to allow any machine shop with a multi-axis Computer Numerical Control (CNC) machine to fabricate the piece parts from commonly available materials. In line with the goals of LCOT, the monitor and control functions are developed as a modular and flexible system with the ability to support future hardware or algorithm changes, minimizing disruptions. A main priority of development in the Monitor and Control Subsystem (MCS) is the safety monitor system.

laser communication↗

NASA NTRSDate not supplied

Development of a Ground Multi-mission Low Cost Optical Terminal(LCOT) for Free-Space Optical Communication

Once confined to the realm of laboratory experiments and theoretical papers, space-based laser communications (lasercomm) are on the verge of achieving mainstream status. Organizations from Facebook to NASA, and missions from cubesats to Orion are employing lasercomm to achieve gigabit communication speeds at mass and power requirements lower than that of traditional radio frequency (RF) methods. Since first demonstrating free-space optical communications services with Lunar Laser Communications Demonstration (LLCD) in 2013, NASA has invested in developing optical communications technologies and capabilities to enhancing its space communications networks. Along with evolving optical space terminals, NASA is also developing lasercomm grounds stations capable of meeting the rapidly increasing data volume demands of upcoming missions, from low-earth to lunar orbits and beyond and integrating these advanced capabilities into its Near-Space and Deep Space Networks. To meet this emerging need, the Low-Cost Optical Terminal (LCOT) project at NASA’s Goddard Space Flight Center (GSFC) is designing, building and validating a prototype for a flexible, multi-mission, and economical optical ground terminal that could be used as a blueprint for a global network of optical ground stations, capable of supporting a wide variety of missions. To date a major impediment to widespread adoption of laser communication has been the lack of an existing ground network infrastructure. A mission that wishes to take advantage of laser communication not only needs to invest in an optical space terminal, but it must also finance the creation of ground terminals to receive the downlink signal. This adds significant additional cost. Missions that do decide to incur the cost of financing a network of ground terminals end up building highly specialized optical receivers that are operable as receivers for that specific mission only. Significant Non-Recurring Engineering (NRE) cost is invested to build highly specialized one-of-a-kind ground terminals that go into storage after that particular mission is over. This is not an economical approach and does nothing to grow the number of optical ground stations available to future missions. In essence each mission that wants to take advantage of the benefits of lasercom has to start from scratch to provide a ground terminal network to support it. As long as this is the case, the cost for using laser communications will be too high for most missions to consider. LCOT intends to close this gap in technology by designing and developing a standard optical ground terminal design that is flexible enough to serve as a receiver for a wide range of future missions – a ground terminal that can be quickly reconfigured to receive downlinks at different wavelengths using different signal formats. Not only does LCOT have the industry-building objectives of utilizing commercial-off-the-shelf (COTS) components to the maximum extent possible, but also spurs the commercial development of other necessary lasercomm components not currently offered by industry. Finally, LCOT will give NASA scientists and engineers a facility where they can gain real-world experience with optical communications. It will give engineers a cost-effective way to try out new concepts and processes by providing the infrastructure for such testing. In this way it is hoped LCOT will serve as a stimulus for innovation in optical communications and speed its widespread adoption by future missions. The LCOT is comprised of five subsystems: Free-Space Optical, Transceiver, Amplifier, Monitor and Control, and Observatory Infrastructure. In August 2021, the LCOT team installed a 70 cm telescope, developed by Planewave Instruments that was optimized for optical communications. Free-Space Optical subsystem comprises of the telescope and its associated hardware, including a transmitter optical assembly, wide field cameras, two optical benches, and an adaptive optics subsystem. The transmit optical assembly, a unique concept design, is a cluster of four functionally independent transmit subassemblies located on the receive telescope. In addition to receiving optical signals and directing the expanded beam with high precision to the space terminal, it also performs tracking functions. The transmit optical assembly will support operations from Low Earth Orbit (LEO) through lunar and will be used as a template for industry manufacturing. The Optical Infrastructure subsystem is responsible for providing environmentally controlled shelters for LCOT equipment and various other systems. To maintain the safety and proper functionality of the telescope, a 16 ft Astrohaven clamshell dome procured which provides all-sky coverage without the need to rotate the dome. Additionally, Atmospheric Monitoring Assembly (AMA) will be part of optical infrastructure subsystem to ensure accurate performance of the LCOT. Like existing optical ground stations, LCOT will measure standard weather station parameters, infrared all sky image of cloud cover, and cloud height. LCOT, however, adds requirements for measuring night time seeing and, in the future, daytime seeing. Unlike other optical ground terminals, the LCOT is transceiver agnostic; user transceivers may be duplex transceivers, standalone receivers, or standalone transmitters with or without acquisition beacon functionality. As such, the LCOT project accommodates testing with external customer transceivers in a flexible manor, further complimenting its intended multi-mission goals. Another unique component of LCOT is the use of a new amplifier technology – the Very Large Mode Area (VLMA) amplifiers. This new technology allows LCOT to avoid the issues faced by previous laser communications ground terminals, gives users more flexibility and modular capability, and is capable of reaching an order of magnitude higher peak power than traditional High Power Optical Amplifiers (HPOA). One drawback of the VLMA HPOA approach is that the amplified light is output into free-space. The solution developed by LCOT is an optics train that couples the output of the VLMA amplifier into a short fiber for transport to the transmit telescopes with high efficiency. Like many of the LCOT components, a set of detailed manufacturing drawings have been created for the optics train to allow any machine shop with a multi-axis Computer Numerical Control (CNC) machine to fabricate the piece parts from commonly available materials. In line with the goals of LCOT, the monitor and control functions are developed as a modular and flexible system with the ability to support future hardware or algorithm changes, minimizing disruptions. A main priority of development in the Monitor and Control Subsystem (MCS) is the safety monitor system.

Haleh Safavi↗