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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Linear system identification via backward-time observer models

This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.

Juang, Jer-Nan↗
NASA NTRS1957

Comparison of several methods for obtaining the time response of linear systems to either a unit impulse or arbitrary input from frequency-response data

Several methods of obtaining the time response of Linear systems to either a unit impulse or an arbitrary input from frequency-response data are described and compared. Comparisons indicate that all the methods give good accuracy when applied to a second-order system; the main difference is the required computing time. The methods generally classified as inverse Laplace transform methods were found to be most effective in determining the response to a unit impulse from frequency-response data of higher order systems. Some discussion and examples are given of the use of such methods as flight-data-analysis techniques in predicting loads and motions of a flexible aircraft on the basis of simple calculations when the aircraft frequency response is known.

Donegan, James J↗
DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

A method to stabilize linear systems using eigenvalue gradient information

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Wieseman, C. D.↗
NASA NTRS1991

Polynomial Transformations For Discrete-Time Linear Systems

Transformations based on polynomial matrices of finite degree developed for use in computing functions for compensation, inversion, and approximation of discrete-time, multivariable, linear systems. Method derived from z-transform transfer-function form of matrices. Applicable to cascade-compensation problems in design of control systems.

Baram, Yoram↗
NASA NTRS1990

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Freund, Roland W.↗
NASA NTRS1990

Fast secant methods for the iterative solution of large nonsymmetric linear systems

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

Deuflhard, Peter↗
NASA NTRS1992

Identifiability of linear systems in physical coordinates

Identifiability of linear, time-invariant systems in physical coordinates is discussed. It is shown that identification of the system matrix in physical coordinates can be accomplished by determining a transformation matrix that relates the physical locations of actuators and sensors to the test-data-derived input and output matrices. For systems with symmetric matrices, the solution of a constrained optimization problem is used to characterize all the possible solutions of the transformation matrix. Conditions for the existence of a unique transformation matrix are established easily from the explicit form of the solutions. For systems with limited inputs and outputs, the question about which part of the system can be uniquely identified is also answered. A simple mass-spring system is used to verify the conclusions of this study.

Su, Tzu-Jeng↗
NASA NTRS1980

A scaling theory for linear systems

A theory of scaling for rational (transfer) functions in terms of transformation groups is developed. Two different four-parameter scaling groups which play natural roles in studying linear systems are identified and the effect of scaling on Fisher information and related statistical measures in system identification are studied. The scalings considered include change of time scale, feedback, exponential scaling, magnitude scaling, etc. The scaling action of the groups studied is tied to the geometry of transfer functions in a rather strong way as becomes apparent in the examination of the invariants of scaling. As a result, the scaling process also provides new insight into the parameterization question for rational functions.

Brockett, R. W.↗
NASA NTRS1975

Design of optimal partial state feedback controllers for linear systems in stochastic environments

The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.

Joshi, S. M.↗
NASA NTRS1990

Upper and lower covariance bounds for perturbed linear systems

Both upper and lower bounds are established for state covariance matrices under parameter perturbations of the plant. The motivation for this study lies in the fact that many robustness properties of linear systems are given explicitly in terms of the state covariance matrix. Moreover, there exists a theory for control by covariance assignment. The results provide robustness properties of these covariance controllers.

Xu, J.-H.↗
NASA NTRS1990

On lightly damped linear systems

A simple engineering approximation using undamped modes is shown to be valid for determining the effect of small viscous or equivalent viscous-type damping forces on the forced vibration response of a lightly damped linear systems. It is shown that intermodal coupling of the undamped modes may be neglected with negligible error, except when the system has degenerate or quasi-degenerate modes. This can occur in complex structural systems such as aircraft or spacecraft. In such cases, one of these two modes has virtually no damping, whereas the other effectively has the damping of both.

Young, M. I.↗
NASA NTRS1987

Solving very large, sparse linear systems on mesh-connected parallel computers

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

Opsahl, Torstein↗
NASA NTRS1999

Asymptotic Stability of Interconnected Passive Non-Linear Systems

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

Isidori, A.↗
NASA NTRS2021

Linear Systems LSK389 and LSK489 Dual N-Channel JFET Amplifier Total Ionizing Dose and Single-Event Effects Test Report

The purpose of these tests was to characterize the susceptibility of the LSK389 and LSK489 Dual N-Channel JFET from Linear Systems to Single-Event Latchup due to heavy ions and to Total Ionizing Dose (TID) degradation at -65 °C and intermediate dose rate. The test was carried out to assess suitability of the amplifiers for the Ocean Color instrument (OCI) on the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) spacecraft.

Ray Ladbury↗