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Results for “Multivariate optimization”

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 55 records · Page 3
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NASA NTRS2019

Measurement of CH3D on Titan at Submillimeter Wavelengths

We present the first radio/submillimeter detection of monodeuterated methane (CH3D) in Titan's atmosphere, using archival data from of the Atacama Large Millimeter/submillimeter Array (ALMA). The J (sub K) equals 2 (sub 1) minus 1 (sub 1) and J (sub K) equals 2 (sub 0) minus 1 (sub 0) transitions at 465.235 and 465.250 gigahertz (approximately 0.644 millimeters) were measured at significance levels of 4.6 sigma and 5.7 sigma, respectively. These two lines were modeled using the Non-linear optimal Estimator for MultivariatE spectral analySIS (NEMESIS) radiative transfer code to determine the disk-averaged CH3D volume mixing ratio equals 6.157 times 10 (sup minus 6) in Titan's stratosphere (at altitudes greater than 130 kilometers). By comparison with the CH4 vertical abundance profile measured by Cassini-Huygens mass spectrometry, the resulting value for D/H in CH4 is (1.033 plus or minus 0.081) times 10 (sup minus 4). This is consistent with previous ground-based and in situ measurements from the Cassini-Huygens mission, though slightly lower than the average of the previous values. Additional CH3D observations at higher spatial resolution will be required to determine a value truly comparable with the Cassini-Huygens CH4 measurements, by measuring CH3D with ALMA close to Titan's equator. In the post-Cassini era, spatially resolved observations of CH3D with ALMA will enable the latitudinal distribution of methane to be determined, making this an important molecule for further studies.

Thelen, Alexander E.↗
NASA NTRS2022

New Constraints on Titan's Stratospheric n-Butane Abundance

Curiously, n-butane has yet to be detected at Titan, though it is predicted to be present in a wide range of abundances that span over 2.5 orders of magnitude. We have searched infrared spectroscopic observations of Titan for signals from n-butane (n-C4H10) in Titan's stratosphere. Three sets of Cassini Composite Infrared Spectrometer Focal Plane 4 (1050–1500 cm−1) observations were selected for modeling, having been collected from different flybys and pointing latitudes. We modeled the observations with the Nonlinear Optimal Estimator for MultivariatE Spectral AnalySIS radiative transfer tool. Temperature profiles were retrieved for each of the data sets by modeling the ν4 emission from methane near 1305 cm−1. Then, incorporating the temperature profiles, we retrieved abundances of all of Titan's known trace gases that are active in this spectral region, reliably reproducing the observations. We then systematically tested a set of models with varying abundances of n-butane, investigating how the addition of this gas affected the fits. We did this for several different photochemically predicted abundance profiles from the literature, as well as for a constant-with-altitude profile. Ultimately, though we did not produce any firm detection of n-butane, we derived new upper limits on its abundance specific to the use of each profile and to multiple different ranges of stratospheric altitudes. These results will tightly constrain the C4 chemistry of future photochemical modeling of Titan's atmosphere and also motivate the continued search for n-butane and its isomer, isobutane.

Brendan L. Steffens↗
NASA NTRS1982

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

Hargrove, A.↗
NASA NTRS1985

Analysis/forecast experiments with a multivariate statistical analysis scheme using FGGE data

A three-dimensional, multivariate, statistical analysis method, optimal interpolation (OI) is described for modeling meteorological data from widely dispersed sites. The model was developed to analyze FGGE data at the NASA-Goddard Laboratory of Atmospherics. The model features a multivariate surface analysis over the oceans, including maintenance of the Ekman balance and a geographically dependent correlation function. Preliminary comparisons are made between the OI model and similar schemes employed at the European Center for Medium Range Weather Forecasts and the National Meteorological Center. The OI scheme is used to provide input to a GCM, and model error correlations are calculated for forecasts of 500 mb vertical water mixing ratios and the wind profiles. Comparisons are made between the predictions and measured data. The model is shown to be as accurate as a successive corrections model out to 4.5 days.

Baker, W. E.↗
NASA NTRS1990

Total energy control system autopilot design with constrained parameter optimization

A description is given of the application of a multivariable control design method (SANDY) based on constrained parameter optimization to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the direct synthesis of a multiloop AFCS inner-loop feedback control system based on total energy control system (TECS) principles. The design procedure offers a structured approach for the determination of a set of stabilizing controller design gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The approach can be extended to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by proper formulation of the design objectives and constraints. Satisfactory designs are usually obtained in few iterations. Performance characteristics of the optimized TECS design have been improved, particularly in the areas of closed-loop damping and control activity in the presence of turbulence.

Ly, Uy-Loi↗
NASA NTRS1981

An algorithm for the rapid location of an extreme of a function subject only to geometric restrictions

The requirements of symmetry and convexity in the application of algorithms for the minimization or maximization of a function are discussed. It is argued that if a function of a single variable is convex and symmetric in a neighborhood of an extremum, the extremum may be approximated to the precision that increases by at least a power of two per functional evaluation. The procedure may be used to drive a complex optimization procedure in the multivariate area estimation problem encountered in remote sensing.

Terrell, G. R.↗
NASA NTRS1983

Dynamics and control of forward swept wing aircraft

Aspects of non-zero differential game theory with application to multivariable control synthesis and optimal linear control law design using optimum parameter sensitivity analysis are discussed.

Schmidt, D. K.↗
NASA NTRS1985

Robust Control Design for Large Space Structures

The control design problem for the class of future spacecraft referred to as large space structures (LSS) is by now well known. The issue is the reduced order control of a very high order, lightly damped system with uncertain system parameters, particularly in the high frequency modes. A design methodology which incorporates robustness considerations as part of the design process is presented. Combining pertinent results from multivariable systems theory and optimal control and estimation, LQG eigenstructure assignment and LQG frequency shaping, were used to improve singular value robustness measures in the presence of control and observation spillover.

Eastman, W. L.↗
NASA NTRS1989

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Bernstein, Dennis S.↗
NASA NTRS1991

Sequential design of linear quadratic state regulators with prescribed eigenvalues and specified relative stability

This paper considers the problem of optimal regulator design of linear multivariable systems with prescribed pole locations and/or poles corresponding to specified relative stability. A sequential method based on the frequency-domain optimality condition is proposed for achieving the desired pole assignment and determination of the corresponding quadratic performance index. This design method enables the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

Ganesan, Sekar↗
NASA NTRS1992

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett↗
NASA NTRS1978

Design of a compensation for an ARMA model of a discrete time system

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Mainemer, C. I.↗
NASA NTRS1974

Multilevel control optimization using subsystem relative performance index sensitivity

A method is presented for the design of optimal feedback controllers for large multivariable systems with subsystem sensitivity constraints. The weighted sum of subsystem and/or operational mode relative performance index sensitivities is defined as the overall performance index. The method is developed for linear systems with quadratic performance criteria and either full or partial state feedback. An example concerning the design of a stability augmentation system for a VTOL aircraft in the transition mode demonstrates the effectiveness of the design method.

Leininger, G. G.↗
NASA NTRS1991

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Mercadal, Mathieu↗
NASA NTRS1989

Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria

A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.

Rew, D. W.↗
NASA NTRS2004

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

Borovikov, Anna↗