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At least 235 records · Page 13

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NASA NTRS1971

Optimal limited state variable feedback controllers for linear systems.

Optimized static and dynamic linear system compensator designs with a priori fixed dimensions are discussed. Expressions are derived to determine the parameters of these designs, including the fixed-gain output feedback, the time-varying output feedback, and time-invariant compensation. A relevant deterministic off-line optimization problem is formulated, and the properties of a solution to the problem are analyzed. A unified design philosophy for limited state-variable control problems of essentially deterministic systems is developed. The philosophy incorporates design constraints, a careful selection of performance criteria, and interpretation of the results.

Levine, W. S.↗

NASA NTRS1972

Incomplete state feedback for systems with parameter uncertainty and random disturbances

A unified design philosophy is presented for limited state feedback control problems with parameter uncertainty for both deterministic and stochastic problems. Two approaches are considered: linear compensator for the deterministic problem with parameter uncertainty, and for the single input-single output system with parameter uncertainty, a model on order equal to that of the system less the number of zeroes. The limitations of these approaches are discussed along with suggestions for further research.

Basuthakur, S.↗

NASA NTRS1974

Control of Finite-State, Finite Memory Stochastic Systems

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

Sandell, Nils R.↗

NASA NTRS1974

Mathematical crew motion disturbance models for spacecraft control system design

Several techniques for modeling the disturbances to a spacecraft's attitude caused by moving crew members are presented. These disturbances can be the largest moments acting on a manned spacecraft, and knowledge of their effect is important in the sizing, design, and analysis/simulation of spacecraft attitude control systems. The modeling techniques are identified as two principal types: deterministic and stochastic. Three techniques of each type are presented. The deterministic models include point-mass motion derivatives and a discussion on dynamic models of moving crew members. The stochastic techniques are highlighted by a Fourier transform method and the representation of long-term crew disturbance activities as outputs from appropriately designed filters. A z-transform technique is developed to obtain a difference-equation form of stochastic models for use on digital computers. An appendix derives spacecraft equations of motion which can be used with many of the models discussed.

Conway, B. A.↗

NASA NTRS1974

State equations for an n-body spacecraft

Considerable attention, in the open literature, is being focused on the problem of developing a suitable set of deterministic dynamical equations for a complex spacecraft. The present paper addresses the problem of determining a set of state equations for an n-body spacecraft. The approach used in obtaining the state equations involves the application and interpretation of advanced dynamical principles. This set of state equations can be effectively used in the development of a stochastic controller for the spacecraft (in this latter development, the deterministic model developed in the present paper will be appropriately corrupted by plant noise). The major effort in the paper revolves around the determination of the plant matrices and the specification of the state vector and the control vector.

Larson, V.↗

NASA NTRS1976

Position error propagation in the simplex strapdown navigation system

The results of an analysis of the effects of deterministic error sources on position error in the simplex strapdown navigation system were documented. Improving the long term accuracy of the system was addressed in two phases: understanding and controlling the error within the system, and defining methods of damping the net system error through the use of an external reference velocity or position. Review of the flight and ground data revealed error containing the Schuler frequency as well as non-repeatable trends. The only unbounded terms are those involving gyro bias and azimuth error coupled with velocity. All forms of Schuler-periodic position error were found to be sufficiently large to require update or damping capability unless the source coefficients can be limited to values less than those used in this analysis for misalignment and gyro and accelerometer bias. The first-order effects of the deterministic error sources were determined with a simple error propagator which provided plots of error time functions in response to various source error values.

Source record↗

NASA NTRS1976

Shuttle onboard IMU alignment methods

The current approach to the shuttle IMU alignment is based solely on the Apollo Deterministic Method. This method is simple, fast, reliable and provides an accurate estimate for the present cluster to mean of 1,950 transformation matrix. If four or more star sightings are available, the application of least squares analysis can be utilized. The least squares method offers the next level of sophistication to the IMU alignment solution. The least squares method studied shows that a more accurate estimate for the misalignment angles is computed, and the IMU drift rates are a free by-product of the analysis. Core storage requirements are considerably more; estimated 20 to 30 times the core required for the Apollo Deterministic Method. The least squares method offers an intermediate solution utilizing as much data that is available without a complete statistical analysis as in Kalman filtering.

Henderson, D. M.↗

NASA NTRS1976

On optimal control of linear systems in the presence of multiplicative noise

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programming. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an 'enforced separation' solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

Joshi, S. M.↗

NASA NTRS1975

Connective stability of large-scale stochastic systems

The procedure of decomposition-aggregation analysis reported by Siljak (1973) and Grujic and Siljak (1973) has been used in a study of the connective-stability aspects of large-scale stochastic systems. An investigation is conducted of the tolerance of a system of interconnected deterministic subsystems to both deterministic and stochastic interactions. The connective stability in the mean is considered and the connective property of stability is defined. The defined concept is included in a modification of the comparison theorem described by Ladde (1975). Attention is also given to a derivation of the sufficient conditions for the connective stability in the mean.

Ladde, G. S.↗

NASA NTRS1975

Markov information sources

A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.

Massey, J. L.↗

NASA NTRS1977

Geodetic linear estimation technique and the norm choice problem

In this work the mathematical and probabilistic background of standard linear estimation techniques used in geodesy is clarified, and their interrelationship is revealed with the help of best approximation theory and the normal equations. Emphasis is given to the separation of the deterministic solution to the approximation problem from the probabilistic justification of the metric of the approximation. Least squares prediction has been related to deterministic (exact) collocation, and minimum error bound has been identified as a prediction optimality criterion in the latter. Criteria for the optimal choice of norm in Hilbert space collocation are proposed for gravimetric geodesy problems.

Dermanis, A.↗

NASA NTRS1979

Multiple object tracking with non-unique data-to-object association via generalized hypothesis testing

A generalized hypothesis testing approach is applied to the problem of tracking several objects where several different associations of data with objects are possible. Such problems occur, for instance, when attempting to distinctly track several aircraft maneuvering near each other or when tracking ships at sea. Conceptually, the problem is solved by first, associating data with objects in a statistically reasonable fashion and then, tracking with a bank of Kalman filters. The objects are assumed to have motion characterized by a fixed but unknown deterministic portion plus a random process portion modeled by a shaping filter. For example, the object might be assumed to have a mean straight line path about which it maneuvers in a random manner. Several hypothesized associations of data with objects are possible because of ambiguity as to which object the data comes from, false alarm/detection errors, and possible uncertainty in the number of objects being tracked. The statistical likelihood function is computed for each possible hypothesized association of data with objects. Then the generalized likelihood is computed by maximizing the likelihood over parameters that define the deterministic motion of the object.

Porter, D. W.↗

NASA NTRS1978

Random motion analysis of flexible satellite structures

A singular perturbation formulation is used to study the responses of a flexible satellite when random measurement errors can occur. The random variables, at different instants of time, are assumed to be uncorrelated. Procedures for obtaining maxima and minima are described, and a variation of the linear method is developed for the formal solution of the two-point boundary-value problems represented by the variational equations. Random and deterministic solutions for the structural position coordinates are studied, and an analytic algorithm for treating the force equation of motion is developed. Since the random system indicated by the variational equation will always be asymptotically unstable, any analysis of stability must be based on the deterministic system.

Huang, T. C.↗

NASA NTRS1978

A study of parameter identification

A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix.

Herget, C. J.↗

NASA NTRS1983

Predictions of the structure of turbulent, particle-laden, round jets

Models of gas and particle motion in turbulent, particle-laden, round jets were evaluated using existing measurements of flow structure. Three models were considered: (1) a locally homogeneous flow model, where velocities and turbulent mixing properties of both phases were assumed to be equal; (2) a deterministic separated flow model, where interphase slip was considered but effects of turbulent dispersion were ignored; and (3) a stochastic separated flow model where effects of interphase slip and turbulent dispersion were considered using random sampling techniques. In all three cases, mean and turbulent properties of the continuous phase were found with a well-calibrated k-epsilon model. The locally homogeneous flow and deterministic separated flow models over- and underestimated particle spread and flow development rates, respectively. The stochastic separated flow model, however, yielded satisfactory predictions of flow structure - except at high particle loadings. Uncertainties in initial conditions for the measurements and possible effects of turbulence modulation by the particles are proposed as the reason for these errors.

Shuen, J.-S.↗

NASA NTRS1983

Simplified analysis techniques to support the determination of Shuttle aerodynamics

The use of deterministic and regression methods to supplement the maximum likelihood estimation programs for the determination of the stability and control parameters of the Shuttle vehicle is discussed. Examples taken from STS-2 and STS-3 flight data show the use of deterministic methods to verify the effectiveness of the pitch and roll Reaction Control System (RCS), to verify the model structure used in the maximum likelihood estimator and to indicate regions of the descent trajectory where unmodeled moments dominate the vehicle motion and the application of maximum likelihood estimation would lead to incorrect parameter values. The use of regression methods to determine selected parameters when the more sophisticated maximum likelihood programs are not required, to determine the form of the vehicle mathematical model and to select the data time intervals for most effective parameter identification are also discussed.

Suit, W. T.↗

NASA NTRS1985

An error-dependent model of instrument-scanning behavior in commercial airline pilots

A new flexible model of pilot instrument scanning behavior is presented which assumes that the pilot uses a set of deterministic scanning patterns on the pilot's perception of error in the state of the aircraft, and the pilot's knowledge of the interactive nature of the aircraft's systems. Statistical analyses revealed that a three stage Markov process composed of the pilot's three predicted lookpoints (LP), occurring 1/30, 2/30, and 3/30 of a second prior to each LP, accurately modelled the scanning behavior of 14 commercial airline pilots while flying steep turn maneuvers in a Boeing 737 flight simulator. The modelled scanning data for each pilot were not statistically different from the observed scanning data in comparisons of mean dwell time, entropy, and entropy rate. These findings represent the first direct evidence that pilots are using deterministic scanning patterns during instrument flight. The results are interpreted as direct support for the error dependent model and suggestions are made for further research that could allow for identification of the specific scanning patterns suggested by the model.

Jones, D. H.↗

NASA NTRS1985

Efficient algorithms for use in probabilistic finite element analysis

This paper investigates the use of Fast Probability Integration (FPI) algorithms in a Finite Element environment. A method allowing the representation of correlated fields in terms of a vector of uncorrelated transformed variables, based on the spectral decomposition of the variance-covariance matrix is developed. The response of the deterministic model corresponding to selected perturbations of these uncorrelated variables is then obtained via a Newton-type iterative scheme. The results of the perturbed problems are used to construct a local representation of the model's behavior in the neighborhood of the deterministic state, which the FPI algorithm will use to estimate the reliability of the system. Although the proposed strategy has thus far only been applied to linear elastostatics, the extension of the method to a broader class of problems appears to be feasible.

Dias, J. B.↗