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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Stochastic Robustness: Towards a Comprehensive Robustness Tool

Stochastic robustness is a simple technique to determine the robustness of linear, time-invariant systems by Monte Carlo methods. Stochastic stability robustness has been described previously. Those results are extended here to provide insight into control system design for performance. Together, stochastic stability and performance robustness concepts constitute a comprehensive tool that can be used to analyze control system robustness properties. As well, they offer control system design insight that can set the stage for stochastic robustness synthesis. The concept of stochastic stability robustness is reviewed, stochastic performance robustness is introduced, and stochastic robustness synthesis is described qualitatively. Confidence intervals necessary for comparing control laws statistically are presented.

Ray, Laurie Ryan↗
NASA NTRS1997

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS1997

Detection of "noisy" chaos in a time series

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS1972

Application of a stochastic inverse to the geophysical inverse problem

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Jordan, T. H.↗
NASA NTRS1973

Control optimization, stabilization and computer algorithms for aircraft applications

Computationally useful algorithms are considered that can aid the control engineer in designing systems control in linear time invariant dynamics for aircraft applications. Structural aspects of system identification, matrix parameterization, and the effect of feedback on identifiability of systems. Adaptive and stochastic control model constructions are projected, and a method for approximate identification of aircraft characteristics and subsequent generation of control signals is outlined.

Mitter, S. K.↗
NASA NTRS1974

Approximations to and local properties of diffusions with discontinuous controls

The paper discusses several properties of control systems defined by stochastic differential equations, which are defined by the method of Girsanov, using a transformation of measures, and where the controls are discontinuous. Uniqueness of the multivariate distributions of the process is proved, and it is shown that the process is a limit, in a natural sense, of a certain discrete time approximation. Other questions, concerning the effects on the distributions of the paths, and of the cost of approximating the control by a smooth control and concerning local properties of the solution, are discussed.

Kushner, H. J.↗
NASA NTRS1985

Pioneer 10 search for gravitational waves - Limits on a possible isotropic cosmic background of radiation in the microhertz region

The nature of the response of the Doppler tracking system to a stochastic background of gravitational radiation is discussed. Using data acquired in 1981 by the Deep Space Network with the Pioneer 10 spacecraft, interesting upper limits are placed on the energy density of the background in three frequency bands extending from 7 x 10 to the -7th to 10 to the -4th Hz, a region that has been inaccessible previously by any technique.

Anderson, J. D.↗
NASA NTRS1985

Dynamic features of combustion

The dynamic features of combustion are discussed for four important cases: ignition, inflammation, explosion, and detonation. Ignition, the initiation of a self-sustained exothermic process, is considered in the simplest case of a closed thermodynamic system and its stochastic distribution. Inflammation, the initiation and propagation of self-sustained flames, is presented for turbulent flow. Explosion, the dynamic effects caused by the deposition of exothermic energy in a compressible medium, is illustrated by self-similar blast waves with energy deposition at the front and the adiabatic non-self-similar wave. Detonation, the most comprehensive illustration of all the dynamic effects of combustion, is discussed with a phenomenological account of the development and structure of the wave.

Oppenheim, A. K.↗
NASA NTRS2000

Stardust Navigation Covariance Analysis

The Stardust spacecraft was launched on February 7, 1999 aboard a Boeing Delta-II rocket. Mission participants include the National Aeronautics and Space Administration (NASA), the Jet Propulsion Laboratory (JPL), Lockheed Martin Astronautics (LMA) and the University of Washington. The primary objective of the mission is to collect in-situ samples of the coma of comet Wild-2 and return those samples to the Earth for analysis. Mission design and operational navigation for Stardust is performed by the Jet Propulsion Laboratory (JPL). This paper will describe the extensive JPL effort in support of the Stardust pre-launch analysis of the orbit determination component of the mission covariance study. A description of the mission and it's trajectory will be provided first, followed by a discussion of the covariance procedure and models. Predicted accuracy's will be examined as they relate to navigation delivery requirements for specific critical events during the mission. Stardust was launched into a heliocentric trajectory in early 1999. It will perform an Earth Gravity Assist (EGA) on January 15, 2001 to acquire an orbit for the eventual rendezvous with comet Wild-2. The spacecraft will fly through the coma (atmosphere) on the dayside of Wild-2 on January 2, 2004. At that time samples will be obtained using an aerogel collector. After the comet encounter Stardust will return to Earth when the Sample Return Capsule (SRC) will separate and land at the Utah Test Site (UTTR) on January 15, 2006. The spacecraft will however be deflected off into a heliocentric orbit. The mission is divided into three phases for the covariance analysis. They are 1) Launch to EGA, 2) EGA to Wild-2 encounter and 3) Wild-2 encounter to Earth reentry. Orbit determination assumptions for each phase are provided. These include estimated and consider parameters and their associated a-priori uncertainties. Major perturbations to the trajectory include 19 deterministic and statistical maneuvers planned for the mission. The spacecraft is three axis stabilized and has unbalanced thrusters for attitude control. Accelerations due to the attitude control system are treated stochastically. The tracking scenario for the study is patterned after the actual schedule employed during the different phases of the mission. Conventional X-band two-way Doppler and SRA range data was simulated and the standard accuracy for these data types was assumed throughout most of the mission. However, a deweighting scheme was used for the Doppler data during times of low Sun-Earth-Probe angles, especially in the case of the DSM. Optical data is assumed to be available starting at 50 days prior to the comet encounter. The optical data will be used to improve the ephemeris of Wild-2, which is considered crucial to properly target the comet flyby. Results of the covariance analysis are presented for all mission phases. Navigation capability will be discussed in terms of the uncertainty in the encounter B-Plane (B.R and B.T) and linearized time of flight. Delivery errors based on the final maneuver prior to the comet encounter will be presented. The most stringent navigation requirement is for the Earth reentry. The uncertainty in the flight path angle must be less than 0.02 degree (orbit determination and maneuver performance) to assure successful recovery of the SRC. Results presented show that this requirement can be met.

Menon, Premkumar R.↗
NASA NTRS1989

A new adaptive control approach for aerospace vehicles with parameter uncertainties

A new stochastic adaptive control structure is developed for the problem of combined parameter estimation and control of aerospace vehicles with changing parameters. Parameter uncertainties are modeled as first-order Gauss-Markov processes, and are introduced to the system dynamics through a small parameter. It is assumed that an accurate inertial measurement unit gives perfect measurements of the state variables. Since the stochastic system is assumed to be Gauss-Markov, the density function of the parameters given these measurements is conditionally Gaussian. Based on this conditionally Gaussian density, the problem of minimizing a quadratic cost over an infinite time horizon can be set up within the framework of stochastic optimal control theory. The optimal feedback control law is derived from a straightforward expansion of the Hamilton-Jacobi-Bellman equation, based on the LQG solution. The resulting nonlinear controller is applied to the pitch axis control of a space platform with uncertain moments of inertia and is shown to produce marked improvement over a fixed controller.

Hahn, Yungsun↗
NASA NTRS1993

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Goad, Clyde C.↗
NASA NTRS1980

Stochastic analysis of multiple-passband spectral classifications systems affected by observation errors

The classification of targets viewed by a pushbroom type multiple band spectral scanner by algorithms suitable for implementation in high speed online digital circuits is considered. A class of algorithms suitable for use with a pipelined classifier is investigated through simulations based on observed data from agricultural targets. It is shown that time distribution of target types is an important determining factor in classification efficiency.

Tsokos, C. P.↗