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NASA NTRSDate not supplied

A Comparison of Model Predictive Control Architectures for Application to Electrified Aircraft Propulsion Systems

As electrified aircraft propulsion (EAP) systems continue to mature, more sophisticated hardware and software are being developed to balance operations among electric machines and gas-turbine engines. In hybrid-electric propulsion systems, the increased complexity resulting from integrating turbine-engine shafts with electric machines necessitates control methodologies to account for various physical domains. Ideal controllers for hybrid-electric engines manage systems, subsystems, and their interactions in a coordinated fashion, able to account for safety and performance goals while being computationally efficient. In a previous work, linear model predictive control (MPC) schemes were implemented in centralized and distributed frameworks on a nonlinear turbofan engine model as a proof of concept. However, these schemes were not evaluated for computational complexity, prompting further study. The research presented here develops hierarchical MPC schemes to reduce the computational burden of the previous MPC schemes. A two-tier framework is implemented, where a slower sampling MPC controls electric machines and determines fan-speed tracking goals for a faster sampling controller, which is either a MPC or a proportional-integral (PI) controller. The proposed designs are compared to the centralized MPC investigated previously, and performance is measured via fan speed tracking error, energy storage state-of-charge, and computation time. Results reveal that the hierarchical MPC scheme employing a lower-level PI controller improves computation time while maintaining comparable tracking and state-of-charge regulation to the centralized scheme.

model predictive control↗
NASA NTRSDate not supplied

A Comparison of Model Predictive Control Architectures for Application to Electrified Aircraft Propulsion Systems

As electrified aircraft propulsion (EAP) systems continue to mature, more sophisticated hardware and software are being developed to balance operations among electric machines and gas-turbine engines. In hybrid-electric propulsion systems, the increased complexity resulting from integrating turbine-engine shafts with electric machines necessitates control methodologies to account for various physical domains. Ideal controllers for hybrid-electric engines manage systems, subsystems, and their interactions in a coordinated fashion, able to account for safety and performance goals while being computationally efficient. In a previous work, linear model predictive control (MPC) schemes were implemented in centralized and distributed frameworks on a nonlinear turbofan engine model as a proof of concept. However, these schemes were not evaluated for computational complexity, prompting further study. The research presented here develops hierarchical MPC schemes to reduce the computational burden of the previous MPC schemes. A two-tier framework is implemented, where a slower sampling MPC controls electric machines and determines fan-speed tracking goals for a faster sampling controller, which is either a MPC or a proportional-integral (PI) controller. The proposed designs are compared to the centralized MPC investigated previously, and performance is measured via fan speed tracking error, energy storage state-of-charge, and computation time. Results reveal that the hierarchical MPC scheme employing a lower-level PI controller improves computation time while maintaining comparable tracking and state-of-charge regulation to the centralized scheme.

model predictive control↗
NASA NTRS1990

Isolated galaxies, pairs, and groups of galaxies

The authors searched for isolated galaxies, pairs and groups of galaxies in the CfA survey (Huchra et al. 1983). It was assumed that the distances to galaxies are given by R = V/H sub o, where H sub o = 100 km s(exp -1) Mpc(exp -1) and R greater than 6 Mpc. The searching procedure is close to those, applied to find superclusters of galaxies (Kalinkov and Kuneva 1985, 1986). A sphere with fixed radius r (asterisk) is described around each galaxy. The mean spatial density in the sphere is m. Let G (sup 1) be any galaxy and G (sup 2) be its nearest neighbor at a distance R sub 2. If R sub 2 exceeds the 95 percent quintile in the distribution of the distances of the second neighbors, then G (sup 1) is an isolated galaxy. Let the midpoint of G (sup 1) and G (sup 2) be O sub 2 and r sub 2=R sub 2/2. For the volume V sub 2, defined with the radius r sub 2, the density D sub 2 less than k mu, the galaxy G (sup 2) is a single one and the procedure for searching for pairs and groups, beginning with this object is over and we have to pass to another object. Here the authors present the groups - isolated and nonisolated - with n greater than 3, found in the CfA survey in the Northern galactic hemisphere. The parameters used are k = 10 and r (asterisk) = 5 Mpc. Table 1 contains: (1) the group number, (2) the galaxy, nearest to the multiplet center, (3) multiplicity n, (4) the brightest galaxy if it is not listed in (2); (5) and (6) are R.A. and Dec. (1950), (7) - mean distance D in Mpc. Further there are the mean density rho (8) of the multiplet (galaxies Mpc (exp -3), (9) the density rho (asterisk) for r (asterisk) = 5 Mpc and (10) the density rho sub g for the group with its nearest neighbor. The parenthesized digits for densities in the last three columns are powers of ten.

Kuneva, I.↗
NASA NTRS1988

An adaptive identification and control scheme for large space structures

A unified identification and control scheme capable of achieving space at form performance objectives under nominal or failure conditions is described. Preliminary results are also presented, showing that the methodology offers much promise for effective robust control of large space structures. The control method is a multivariable, adaptive, output predictive controller called Model Predictive Control (MPC). MPC uses a state space model and input reference trajectories of set or tracking points to adaptively generate optimum commands. For a fixed model, MPC processes commands with great efficiency, and is also highly robust. A key feature of MPC is its ability to control either nonminimum phase or open loop unstable systems. As an output controller, MPC does not explicitly require full state feedback, as do most multivariable (e.g., Linear Quadratic) methods. Its features are very useful in LSS operations, as they allow non-collocated actuators and sensors. The identification scheme is based on canonical variate analysis (CVA) of input and output data. The CVA technique is particularly suited for the measurement and identification of structural dynamic processes - that is, unsteady transient or dynamically interacting processes such as between aerodynamics and structural deformation - from short, noisy data. CVA is structured so that the identification can be done in real or near real time, using computationally stable algorithms. Modeling LSS dynamics in 1-g laboratories has always been a major impediment not only to understanding their behavior in orbit, but also to controlling it. In cases where the theoretical model is not confirmed, current methods provide few clues concerning additional dynamical relationships that are not included in the theoretical models. CVA needs no a priori model data, or structure; all statistically significant dynamical states are determined using natural, entropy-based methods. Heretofore, a major limitation in applying adaptive controllers to LSS problems has been the requirement for accurate models. We feel that MPC coupled with the CVA identification scheme will resolve this limitation. The results are based on research performed under an SBIR grant, administered by the Air Force Office of Scientific Research.

Carroll, J. V.↗
NASA NTRS1994

Power spectrum, correlation function, and tests for luminosity bias in the CfA redshift survey

We describe and apply a method for directly computing the power spectrum for the galaxy distribution in the extension of the Center for Astrophysics Redshift Survey. Tests show that our technique accurately reproduces the true power spectrum for k greater than 0.03 h Mpc(exp -1). The dense sampling and large spatial coverage of this survey allow accurate measurement of the redshift-space power spectrum on scales from 5 to approximately 200 h(exp -1) Mpc. The power spectrum has slope n approximately equal -2.1 on small scales (lambda less than or equal 25 h(exp -1) Mpc) and n approximately -1.1 on scales 30 less than lambda less than 120 h(exp -1) Mpc. On larger scales the power spectrum flattens somewhat, but we do not detect a turnover. Comparison with N-body simulations of cosmological models shows that an unbiased, open universe CDM model (OMEGA h = 0.2) and a nonzero cosmological constant (CDM) model (OMEGA h = 0.24, lambda(sub zero) = 0.6, b = 1.3) match the CfA power spectrum over the wavelength range we explore. The standard biased CDM model (OMEGA h = 0.5, b = 1.5) fails (99% significance level) because it has insufficient power on scales lambda greater than 30 h(exp -1) Mpc. Biased CDM with a normalization that matches the Cosmic Microwave Background (CMB) anisotropy (OMEGA h = 0.5, b = 1.4, sigma(sub 8) (mass) = 1) has too much power on small scales to match the observed galaxy power spectrum. This model with b = 1 matches both Cosmic Background Explorer Satellite (COBE) and the small-scale power spect rum but has insufficient power on scales lambda approximately 100 h(exp -1) Mpc. We derive a formula for the effect of small-scale peculiar velocities on the power spectrum and combine this formula with the linear-regime amplification described by Kaiser to compute an estimate of the real-space power spectrum. Two tests reveal luminosity bias in the galaxy distribution: First, the amplitude of the pwer spectrum is approximately 40% larger for the brightest 50% of galaxies in volume-limited samples that have M(sub lim) greater than M*. This bias in the power spectrum is independent of scale, consistent with the peaks-bias paradigm for galaxy formation. Second, the distribution of local density around galaxies shows that regions of moderate and high density contain both very bright (M less than M* = -19.2 + 5 log h) and fainter galaxies, but that voids preferentially harbor fainter galaxies (approximately 2 sigma significance level).

Park, Changbom↗
NASA NTRS1994

Velocity correlations of galaxy clusters

We determine the velocity correlation function, pairwise peculiar velocity difference, and rms pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cosmological models: Omega = 1 and Omega = 0.3 cold dark matter (CDM), and Omega = 0.3 primeval baryonic isocurvature (PBI) models (all flat and Cosmic Background Explorer (COBE)-normalized). We find that close cluster pairs, with separation r is less than or equal to 10/h Mpc, exhibit strong attractive peculiar velocities in all models; the cluster pairwise velocities depend sensitively on the model. The mean pairwise attractive velocity of clusters on 5/h Mpc scale ranges from approximately 1700 km/s for Omega = 1 CDM to approximately 1000 km/s for PBI to approximately 700 km/s for Omega = 0.3 CDM. The small-scale pairwise velocities depend also on cluster mass: richer, more massive clusters exhibit stronger attractive velocities than less massive clusters. On large scales, from approximately 20 to 200/h Mpc, the cluster peculiar velocities are increasingly dominated by bulk and random motions; they are independent of cluster mass. The cluster velocity correlation function is negative on small scales for Omega = 1 and Omega = 0.3 CDM, indicating strong pairwise motion relative to bulk motion on small scales; PBI exhibits relatively larger bulk motions. The cluster velocity correlation function is positive on very large scales, from r approximately 10/h Mpc to r approximately 200/h Mpc, for all models. These positive correlations, which decrease monotonically with scale, indicate significant bulk motions of clusters up to approximately 200/h Mpc. The strong dependence of the cluster velocity functions on models, especially at small separations, makes them useful tools in constraining cosmological models when compared with observations.

Cen, Renyue↗
NASA NTRS2008

Intelligent Engine Systems: Adaptive Control

We have studied the application of the baseline Model Predictive Control (MPC) algorithm to the control of main fuel flow rate (WF36), variable bleed valve (AE24) and variable stator vane (STP25) control of a simulated high-bypass turbofan engine. Using reference trajectories for thrust and turbine inlet temperature (T41) generated by a simulated new engine, we have examined MPC for tracking these two reference outputs while controlling a deteriorated engine. We have examined the results of MPC control for six different transients: two idle-to-takeoff transients at sea level static (SLS) conditions, one takeoff-to-idle transient at SLS, a Bode power command and reverse Bode power command at 20,000 ft/Mach 0.5, and a reverse Bode transient at 35,000 ft/Mach 0.84. For all cases, our primary focus was on the computational effort required by MPC for varying MPC update rates, control horizons, and prediction horizons. We have also considered the effects of these MPC parameters on the performance of the control, with special emphasis on the thrust tracking error, the peak T41, and the sizes of violations of the constraints on the problem, primarily the booster stall margin limit, which for most cases is the lone constraint that is violated with any frequency.

Gibson, Nathan↗
NASA NTRSDate not supplied

Model Predictive Control Study for an Electrified Turbofan Engine

A control sensitivity study is conducted for electrified aircraft propulsion concepts using a publicly available turbofan engine simulation. A Proportional-Integral (PI) controller serves as a baseline for comparison against an advanced Model Predictive Control (MPC) approach. MPC is used in the control scheme to allow for subsystem coordination of engine and electric power loads. The electrified turbofan engine includes electric machines to augment the amount of torque being applied to the spools of the engine during transient phases of operation. Power augmentation allows for energy to be stored or exhausted in a manner that increases the fuel efficiency of the engine, reducing aircraft emissions and noise. The study compares the fan speed, high pressure compressor stall margin, and low pressure compressor stall margin against the baseline PI control system, an MPC system without electric machines, and an MPC system with electric machines. The MPC system with electric machines is optimized using the sample time, control horizon and prediction horizon. The MPC design provided a stable damped response as desired and allowed operability margins to be maintained

Electrified Aircraft Propulsion↗
NASA NTRS1993

Complex QSO absorbers: High-redshift clusters of galaxies?

Using the PSPC instrument on the ROSAT satellite, we have obtained deep exposures of the fields centered on the QSO's 1556+335, 1037-271, and 0854+191 in an effort to search for extended X-ray emission corresponding to complex QSO absorption-line systems (QALS's) that could be indicative of clusters of galaxies at high redshift. The QSO 1556+335 is known to have a pair of complicated C IV absorption systems at z equals 1.610 (Delta v = 988 km/s) and z equals 1.650 (Delta v = 1677 km/s) near the z equals 1.641 QSO redshift. It has been suggested that the absorption may be due to two rich clusters, one containing the QSO itself. The QSO 0854+191 (z(sub em) = 1.89) has 6 strong C IV absorption systems in 2 close groups at z equals 1.2954, 1.2973,1.3019 and z equals 1.3522, 1.3543, 1.3558. Assuming q(sub O) equals 0.5 and H(sub O) equals 50 km/s Mpc(exp -l), the redshift range of this absorption-line cluster corresponds to a radial distance of 44 Mpc. Interestingly, there is a nearby (approximately 30') QSO (0856+189) with a projected separation of 16 Mpc whose redshift (z = 1.29) is similar to that of the absorbing material toward 0854+191. In the case of 1037-271 (Z(sub em) = 2.18), common QALSs have been observed at z equals l.90, 1.96, 2.02, 2.08, and 2.14 (a radial range of 66 Mpc) in its spectrum and that of its neighbor Tol 1038-272 (Z(sub em) = 2.32) whose 18' separation corresponds to a linear distance of 9 Mpc at z approximately equals 2. The length scales implied by the absorbers toward 0854+191 and 1037-271 are interesting in that they suggest structures more akin to superclusters than clusters.

Meyer, David M.↗
NASA NTRS1994

Hot gas in the cold dark matter scenario: X-ray clusters from a high-resolution numerical simulation

A new, three-dimensional, shock-capturing hydrodynamic code is utilized to determine the distribution of hot gas in a standard cold dark matter (CDM) model of the universe. Periodic boundary conditions are assumed: a box with size 85 h(exp -1) Mpc having cell size 0.31 h(exp -1) Mpc is followed in a simulation with 270(exp 3) = 10(exp 7.3) cells. Adopting standard parameters determined from COBE and light-element nucleosynthesis, sigma(sub 8) = 1.05, omega(sub b) = 0.06, and assuming h = 0.5, we find the X-ray-emitting clusters and compute the luminosity function at several wavelengths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. We find that most of the total X-ray emissivity in our box originates in a relatively small number of identifiable clusters which occupy approximately 10(exp -3) of the box volume. This standard CDM model, normalized to COBE, produces approximately 5 times too much emission from clusters having L(sub x) is greater than 10(exp 43) ergs/s, a not-unexpected result. If all other parameters were unchanged, we would expect adequate agreement for sigma(sub 8) = 0.6. This provides a new and independent argument for lower small-scale power than standard CDM at the 8 h(exp -1) Mpc scale. The background radiation field at 1 keV due to clusters in this model is approximately one-third of the observed background, which, after correction for numerical effects, again indicates approximately 5 times too much emission and the appropriateness of sigma(sub 8) = 0.6. If we have used the observed ratio of gas to total mass in clusters, rather than basing the mean density on light-element nucleosynthesis, then the computed luminosity of each cluster would have increased still further, by a factor of approximately 10. The number density of clusters increases to z approximately 1, but the luminosity per typical cluster decreases, with the result that evolution in the number density of bright clusters is moderate in this redshift range, showing a broad peak near z = 0.7, and then a rapid decline above redshift z = 3. Detailed computations of the luminosity functions in the range L(sub x) = 10(exp 40) - 10(exp 44) ergs/s in various energy bands are presented for both cluster central regions and total luminosities to be used in comparison with ROSAT and other observational data sets. The quantitative results found disagree significantly with those found by other investigators using semianalytic techniques. We find little dependence of core radius on cluster luminosity and a dependence of temperature on luminosity given by log kT(sub x) = A + B log L(sub x), which is slightly steeper (B = 0.38) than is indicated by observations. Computed temperatures are somewhat higher than observed, as expected, in that COBE-normalized CDM has too much power on the relevant scales. A modest average temperature gradient is found, with temperatures dropping to 90% of central values at 0.4 h(exp -1) Mpc and 70% of central values at 0.9 h(exp -1) Mpc. Examining the ratio of gas to total mass in the clusters normalized to Omega(sub B) h(exp 2) = 0.015, and comparing with observations, we conclude, in agreement with White (1991), that the cluster observations argue for an open universe.

Kang, Hyesung↗
NASA NTRS1980

The Hercules supercluster. II - Analysis

The almost complete sample of more than 150 redshifts for galaxies brighter than m sub p = 15.8 mag in a 28 square degree field in Hercules by Tarenghi et al. is used to examine the cosmography of a 60,000 cubic Mpc conical volume of space. It contains a supercluster of Abell clusters with a depth of about 100 Mpc, a vacant 'void' also with a depth of about 100 Mpc, and a structure wider than 12 Mpc which could be part of a more extensive system of small groups of galaxies. Properties of individual rich clusters in the Hercules supercluster are derived, but they are uncertain because the clusters merge into one another, so that it is difficult to identify them and their member galaxies unambiguously. However, those regions in Hercules containing the largest proportion of early-type galaxies show the least evidence for gravitational relaxation. A difference may exist between the luminosity function of clusters of galaxies and the luminosity function of the foreground sheet.

Tarenghi, M.↗
NASA NTRS1989

Surface brightness fluctuations and the distance to the Virgo Cluster

Preliminary results from a project to measure the fluxes of giant stars in M32, NGC 3379, and five Virgo Cluster galaxies are presented. Since the Virgo Cluster galaxies are approximately equidistant, variations in observed fluctuation amplitude from galaxy to galaxy can be ascribed to variations in absolute luminosity of the giant stars in the galaxies. Assuming a distance of 0.72 Mpc for M32 and correcting for the color effect in m-bar, the typical brightness of giant stars, distances of 9 Mpc for NGC 3379 and 14 Mpc for Virgo, accurate to about 10 percent, are derived. This is used to find a Hubble constant of 88 km/s/Mpc. The method can be used to measure m-bar in galaxies at least 40-50 Mpc distant.

Tonry, John L.↗
NASA NTRS1990

Observations of surface-brightness fluctuations in Virgo

VRI photometric observations of surface-brightness fluctuation in 13 Virgo Cluster galaxies, M32, and NGC 3379, obtained using an 800 x 800 CCD array on the 4-m telescope at KPNO during March 1989, are reported. The data-reduction techniques are described in detail, and the results are presented in tables and graphs. Particular attention is given to distance estimates derived from the I-band fluctuations: it is shown that NGC 4365 is behind the cluster, while NGC 4468 and NGC 4489 are in the foreground. The average distance to the cluster is found to be 17 + or - 1 Mpc, with H0 = 78 + or - 6 km/sec Mpc; the corresponding values from a direct isochrone calibration are 21 Mpc and 64 + or - 5 km/sec Mpc.

Tonry, John L.↗
NASA NTRS1993

Cluster evolution as a probe of primordial density fluctuations

Although COBE's detection of large angle microwave background anisotropies fixes the amplitude of density fluctuations on length scales k exp -1 approximately = (300-6000) h(exp -1)Mpc, what is crucial for the level of large scale clustering is the amplitude of density fluctuations on scales (5-50) h(exp -1)Mpc. The level of dynamical clustering is usually parameterized by the size of the mass fluctuations in 8 h exp -1 Mpc spheres, sigma sub 8. For the cold dark matter model, COBE gives sigma sub 8 approximately = 1, while models with extra large scale power give sigma sub 8 approximately = 1/2. The most massive clusters of galaxies (greater than or approximately = 10 exp 15 solar mass) form from rare 'peak patches' found in the initial mass density distribution. Their abundance as a function of redshift is a sensitive probe of the wave number band k(exp -1) approx. (3-8) h(exp -1)Mpc, hence of sigma sub 8, and so cluster evolution can discriminate among models allowed by the COBE results. We use our Hierarchical Peaks Method, which accurately reproduces the results of P3M N-body simulations, to calculate the evolution of cluster x-ray flux counts, luminosity, and temperature functions as a function of sigma sub 8 for CDM models and those with more large scale power. We find that the EMSS and Edge et al. cluster samples support sigma sub 8 in the range from approx. 0.6-0.9, and that models with more large scale power (and hence flatter fluctuation spectra in the cluster regime) fit the x-ray bright end better.

Bond, J. Richard↗
NASA NTRS1994

A hydrodynamic approach to cosmology: The mixed dark matter cosmological scenario

We compute the evolution of spatially flat, mixed cold and hot dark matter models containing both baryonic matter and two kinds of dark matter. Hydrodynamics is treated with a highly developed Eulerian hydrodynamic code (see Cen 1992). A standard particle-mesh (PM) code is also used in parallel to calculate the motion of the dark matter components. We adopt the following parameters: h equivalent to (sub 0)/100 km/s Mpc(exp -1) = 0.5, OMEGA(sub C) = 0.3, and OMEGA(sub B) = 0.06, with amplitude of the perturbation spectrum fixed by the Cosmic Background Explorer Satellite (COBE) Dark Matter Radiation (DMR) measurements (Smoot et al. 1992) being sigma (sub 8) = 0.67. Four different boxes are simulated with box sizes of L = (64, 16, 4, 1) h(exp -1) Mpc, respectively, the two small boxes providing good resolution but little valid information due to absence of large-scale power. We use 128(exp 3) approximate 10(exp 6.3) baryonic cells, 128(exp .3) cold dark matter particles, and 2 x 128(exp 3) hot dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H(+), He, He(+), He(++), e(-)) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zeldovich-Sunyaev y parameter is estimated to be y Bar = (5.4 + or - 2.7) x 10(exp -7) below currently attainable observations, with a rms fluctuation of approximately delta bar y = (0.6 + or - 3.0) x 10(exp -7) on arcminute scales. The rate of galaxy formation peaks at an even later epoch (z approximate 0.3) than in the standard (OMEGA = 1, sigma sub 8 = 0.67) cold dark matter (CDM) model (z approximate 0.5) and, at a redshift of z = 4, is nearly a factor of 100 lower than for the CDM model with the same value of sigma sub 8. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of M(sub B) = 10(exp 9.5) solar mass with a reasonable fit to the Schechter luminosity function if the ratio of baryon mass to blue light is approximately 4. In addition, one very large PM simulation was made in a box with size (320 h(exp - 1) Mpc) containing 3 x 200(exp 3) = 10(exp 7.4) particles. Utilizing this simulation we find that the model yields a cluster mass function which is about a factor of 4 higher than observed, but a cluster-cluster correlation length marginally lower than observed, but that both are closer to observations than in the (COBE) normalized CDM model. The one-dimensional pairwise velocity dispersion is 605 + or - 8 km/s at 1/h separation, lower than that of the DCM model normalized to COBE, but still significant higher than observations (Davis & Peebles 1983). A plausible velocity bias b(sub v) = 0.8 + or - 0.1 on this scale will reduce but not remove the discrepancy. The velocity auto-correlat ion function has a coherence length of 40/h Mpc, which is somewhat lower than the observed counterpart. In all these respects the model would be improved by decreasing the cold fraction of the dark OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDB). But formation of galaxies and clusters of galaxies is much later in this model than in COBE-normalized CDM, perhaps too late. To improve on these constraints a larger ratio of OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDM)) is required than the value of 0.67 adopted here. It does not seem possible to find a value for this ratio which would satisfy all tests. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of sigma(sub B), but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter, significantly improves the ability of the COBE-normalized CDM scenario to fit existing observations, but the model is in fact not as good as the CDM model with the same sigma(sub 8) and is still probably unsatisfactory with regard to several critical tests.

Cen, Renyue↗
NASA NTRS1994

Internal velocity and mass distributions in simulated clusters of galaxies for a variety of cosmogonic models

The mass and velocity distributions in the outskirts (0.5-3.0/h Mpc) of simulated clusters of galaxies are examined for a suite of cosmogonic models (two Omega(sub 0) = 1 and two Omega(sub 0) = 0.2 models) utilizing large-scale particle-mesh (PM) simulations. Through a series of model computations, designed to isolate the different effects, we find that both Omega(sub 0) and P(sub k) (lambda less than or = 16/h Mpc) are important to the mass distributions in clusters of galaxies. There is a correlation between power, P(sub k), and density profiles of massive clusters; more power tends to point to the direction of a stronger correlation between alpha and M(r less than 1.5/h Mpc); i.e., massive clusters being relatively extended and small mass clusters being relatively concentrated. A lower Omega(sub 0) universe tends to produce relatively concentrated massive clusters and relatively extended small mass clusters compared to their counterparts in a higher Omega(sub 0) model with the same power. Models with little (initial) small-scale power, such as the hot dark matter (HDM) model, produce more extended mass distributions than the isothermal distribution for most of the mass clusters. But the cold dark matter (CDM) models show mass distributions of most of the clusters more concentrated than the isothermal distribution. X-ray and gravitational lensing observations are beginning providing useful information on the mass distribution in and around clusters; some interesting constraints on Omega(sub 0) and/or the (initial) power of the density fluctuations on scales lambda less than or = 16/h Mpc (where linear extrapolation is invalid) can be obtained when larger observational data sets, such as the Sloan Digital Sky Survey, become available.

Cen, Renyue↗
NASA NTRS2000

Predictive and Neural Predictive Control of Uncertain Systems

Accomplishments and future work are:(1) Stability analysis: the work completed includes characterization of stability of receding horizon-based MPC in the setting of LQ paradigm. The current work-in-progress includes analyzing local as well as global stability of the closed-loop system under various nonlinearities; for example, actuator nonlinearities; sensor nonlinearities, and other plant nonlinearities. Actuator nonlinearities include three major types of nonlineaxities: saturation, dead-zone, and (0, 00) sector. (2) Robustness analysis: It is shown that receding horizon parameters such as input and output horizon lengths have direct effect on the robustness of the system. (3) Code development: A matlab code has been developed which can simulate various MPC formulations. The current effort is to generalize the code to include ability to handle all plant types and all MPC types. (4) Improved predictor: It is shown that MPC design using better predictors that can minimize prediction errors. It is shown analytically and numerically that Smith predictor can provide closed-loop stability under GPC operation for plants with dead times where standard optimal predictor fails. (5) Neural network predictors: When neural network is used as predictor it can be shown that neural network predicts the plant output within some finite error bound under certain conditions. Our preliminary study shows that with proper choice of update laws and network architectures such bound can be obtained. However, much work needs to be done to obtain a similar result in general case.

Kelkar, Atul G.↗
NASA NTRS2020

A Large, Deep 3 Deg2 Survey of Hα, [OIII], and [OII] Emitters from LAGER: Constraining Luminosity Functions

We present our measurements of the Hα, [OIII], and [O II] luminosity functions as part of the Lyman Alpha Galaxies at Epoch of Reionization (LAGER) survey using our samples of 1577 z=0.47Hα-, 3933 z=0.93 [O III]-, and 5367 z=1.59 [O II]-selected emission line galaxies in a 3 deg2 single, CTIO/Blanco DECam pointing of the COSMOS field. Our observations reach 5σ depths of 8.2 × 10−18 erg s−1 cm−2 and comoving volumes of (1−7) × 105 Mpc3 making our survey one of the deepest narrow-band surveys. We select our emission line galaxies via spectroscopic confirmation, photometric redshifts, and colour–colour selections. We measure the observed luminosity functions for each sample and find best fits of φ* = 10−3.16+0.09 −0.09 Mpc−3and L* = 1041.72+0.09 −0.09 erg s−1 for Hα, φ* = 10−2.16+0.10−0.12 Mpc−3 and L* = 1041.38+0.07 −0.06 erg s−1 for [O III], and φ* = 10−1.97+0.07−0.07 Mpc−3 and L* = 1041.66+0.03−0.03 erg s−1 for [OII], with α fixed to −1.75, −1.6, and −1.3, respectively. An excess of bright >1042 erg s−1 [O III] emitters is observed and may be due to active galactic nucleus (AGN) contamination. Corrections for dust attenuation are applied assuming AHα = 1 mag. We also design our own empirical restframe g − r calibration using SDSS DR12 data, test it against our z = 0.47 Hα emitters with zCOSMOS 1D spectra, and calibrate it for (g − r) between −0.8 and 1.3 mag. Dust and AGN corrected star formation rate densities (SFRDs) are measured as log10ρSFR/(Msun yr−1 Mpc−3)=−1.63 ± 0.04, −1.07 ± 0.06, and −0.90 ± 0.10 for Hα, [OIII], and [O II], respectively. We find our [O III] and [O II] samples fully trace cosmic star formation activity at their respective redshifts in comparison to multiwavelength SFRDs, while the Hα sample traces ∼70 per cent of the total z = 0.47 SFRD.

galaxies↗