Harmonic generation of noble-gas atoms in the Near-IR regime using ab-initio time-dependent R-matrix theory

We demonstrate the capability of ab-initio time-dependent R-matrix theory to obtain accurate harmonic generation spectra of noble-gas atoms at Near-IR wavelengths between 1200 and 1800 nm and peak intensities up to 1.8 X 10(14) W/cm(2) . To accommodate the excursion length of the ejected electron, we use an angular-momentum expansion up to Lmax = 279. The harmonic spectra show evidence of atomic structure through the presence of a Cooper minimum in harmonic generation for Kr, and of multielectron interaction through the giant resonance for Xe. The theoretical spectra agree well with those obtained experimentally.Comment: 6 pages, 5 figure

Border Collision Bifurcation Control of Cardiac Alternans

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period doubling border collision bifurcation. No smooth period doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in control laws that quench the bifurcation and hence result in alternan suppression

GPS Based Autonomous Navigation Study for the Lunar Gateway

This paper describes and predicts the performance of a conceptual autonomous GPS-based navigation system for NASA's planned lunar Gateway. This system is based on the flight-proven Magnetospheric Multiscale (MMS) GPS navigation system, augmented with an earth-pointed high-gain antenna and with an option for an atomic clock. High-fidelity simulations, calibrated against MMS flight data and making use of GPS transmitter patterns from the GPS Antenna Characterization Experiment (ACE) project are developed for operation of the system in the Gateway Near-Rectilinear Halo Orbit (NRHO). The results indicate that GPS can provide an autonomous, realtime navigation capability with comparable, or superior, performance to traditional Deep Space Network approach with eight hours of tracking per day

Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems

Feedback control of piecewise smooth discrete-time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasistatically varied. The goal of the control effort in this work is to modify the bifurcation so that the bifurcated steady state is locally attracting and locally unique. To achieve this, Lyapunov-based techniques are used. A sufficient condition for nonbifurcation with persistent stability in piecewise smooth maps of dimension $n$ that depend on a parameter is derived. The derived condition is in terms of linear matrix inequalities. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce desirable behavior

Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems

Feedback controls that stabilize border collision bifurcations are designed for piecewise smooth systems undergoing border collision bifurcations. The paper begins with a summary of the main results on border collision bifurcations, and proceeds to a study of stabilization of these bifurcations for one-dimensional systems using both static and dynamic feedback. The feedback can be applied on one side of the border, or on both sides. To achieve robustness to uncertainty in the border itself, a simultaneous stabilization problem is stated and solved. In this problem, the same control is applied on both sides of the border. Dynamic feedback employing washout filters to maintain fixed points is shown to lead to stabilizability for a greater range of systems than static feedback. The results are obtained with a focus on systems in normal form

Development And Test of A Digitally Steered Antenna Array for The Navigator GPS Receiver

Global Positioning System (GPS)-based navigation has become common for low-Earth orbit spacecraft as the signal environment is similar to that on the Earth s surface. The situation changes abruptly, however, for spacecraft whose orbital altitudes exceed that of the GPS constellation. Visibility is dramatically reduced and signals that are present may be very weak and more susceptible to interference. GPS receivers effective at these altitudes require increased sensitivity, which often requires a high-gain antenna. Pointing such an antenna can pose a challenge. One efficient approach to mitigate these problems is the use of a digitally steered antenna array. Such an antenna can optimally allocate gain toward desired signal sources and away from interferers. This paper presents preliminary results in the development and test of a digitally steered antenna array for the Navigator GPS research program at NASA s Goddard Space Flight Center. In particular, this paper highlights the development of an array and front-end electronics, the development and test of a real-time software GPS receiver, and implementation of three beamforming methods for combining the signals from the array. Additionally, this paper discusses the development of a GPS signal simulator which produces digital samples of the GPS L1C/A signals as they would be received by an arbitrary antenna array configuration. The simulator models transmitter and receiver dynamics, near-far and multipath interference, and has been a critical component in both the development and test of the GPS receiver. The GPS receiver system was tested with real and simulated GPS signals. Preliminary results show that performance improvement was achieved in both the weak signal and interference environments, matching analytical predictions. This paper summarizes our initial findings and discusses the advantages and limitations of the antenna array and the various beamforming methods

New Results on Modal Participation Factors: Revealing a Previously Unknown Dichotomy

The final version of this paper appeared in IEEE Transactions on Automatic Control, Volume 54, Issue 7, July 2009, pp. 1439-1449.This paper presents a new fundamental approach to modal participation analysis of linear time-invariant systems, leading to new insights and new formulas for modal participation factors. Modal participation factors were introduced over a quarter century ago as a way of measuring the relative participation of modes in states, and of states in modes, for linear time-invariant systems. Participation factors have proved their usefulness in the field of electric power systems and in other applications. However, in the current understanding, it is routinely taken for granted that the measure of participation of modes in states is identical to that for participation of states in modes. Here, a new analysis using averaging over an uncertain set of system initial conditions yields the conclusion that these quantities(participation of modes in states and participation of states in modes) should not be viewed as interchangeable. In fact, it is proposed that a new definition and calculation} replace the existing ones for state in mode participation factors, while the previously existing participation factors definition and formula should be retained but viewed only as mode in state participation factors. Examples are used throughout the paper to illustrate the issues addressed and results obtained.National Science Foundation, Office of Naval Research

Predicted Performance of an X-Ray Navigation System for Future Deep Space and Lunar Missions

In November 2017, the NASA Goddard Space Flight Center (GSFC) Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) experiment successfully demonstrated the feasibility of X-ray Pulsar Navigation (XNAV) as part of the Neutron Star Interior Composition Explorer (NICER) mission, which is an X-ray Astrophysics Mission of Opportunity currently operating onboard the International Space Station (ISS). XNAV provides a GPS-like absolute autonomous navigation and timing capability available anywhere in the Solar System and beyond. While the most significant benefits of XNAV are expected to come in support of very deep-space missions, the absolute autonomous navigation and timing capability also has utility for inner Solar System missions where increased autonomy or backup navigation and timing services are required, e.g., address loss of communication scenarios.The NASA commitment to develop a Gateway to support exploration of the Moon and eventually Mars, as well as current and future robotic missions such as James Webb Space Telescope (JWST), New Horizons, and much more, certainly will tax the existing ground based infrastructure in terms of availability. There- fore, an extended look at the feasibility and potential performance of XNAV for comparable missions is warranted. In this paper, we briefly review the XNAV concept and present case studies of its utility and performance for a Gateway orbit, Sun-Earth libration orbit, and a deep space transit trajectory

Feedback Control of Border Collision Bifurcations in Two-Dimensional Discrete-Time Systems

The feedback control of border collision bifurcations is consideredfor two-dimensional discrete-time systems. These are bifurcations that can occur when a fixed point of a piecewise smooth system crosses the border between two regions of smooth operation. The goal of the control effort is to modify the bifurcation so that the bifurcated steady state is locally unique and locally attracting. In this way, the system's local behavior is ensured to remain stable and close to the original operating condition. This is in the same spirit as local bifurcation control results for smooth systems, although the presence of a border complicates the bifurcation picture considerably. Indeed, a full classification of border collision bifurcations isn't available, so this paper focuses on the more desirable (from a dynamical behavior viewpoint) cases for which the theory is complete. The needed results from the analysis of border collision bifurcations are succinctly summarized. The control design is found to lead to systems of linear inequalities. Any feedback gains that satisfy these inequalities is then guaranteed to solve the bifurcation control problem. The results are applied to an example to illustrate the ideas

Instability Monitoring and Control of Power Systems

Today's electric power systems are often subject to stress by heavy loading conditions, resulting in operation with a small margin of stability. This has led to research on estimating the distance to instability. Most of these research efforts are solely model-based. In this work, a signal-based approach for real-time detection of impending instability is considered. The main idea pursued here involves using a small additive white Gaussian noise as a probe signal and monitoring the spectral density of one or more measured states for certain signatures of impending instability. Input-to-state participation factors are introduced as a tool to aid in selection of locations for probe inputs and outputs to be monitored. Since these participation factors are model-based, the chapter combines signal-based and model-based ideas toward achieving a robust methodology for instability monitoring