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Results for “finite-dimensional representation”

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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6 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Model reference control of the NASA SCOLE problem

Model reference controllers have been developed and applied to the linearized Spacecraft Control Laboratory Experiment (SCOLE) roll beam mode equation. When a large- but finite-dimensional approximation to the partial differential equation is used, the resulting control will be finite-dimensional, but possibly not adequately representative for the actual distributed-parameter system. To date the theory for such model reference controllers has been developed; here it is applied to a 16th-order finite-dimensional representation of the flexible and rigid body modes of the SCOLE. Results of the analysis and some preliminary simulation studies are presented.

Kaufman, Howard↗
NASA NTRS1987

Concept of adaptive structures

The concept of adaptive structures is brought up in connection with the need in ultra lightweight structural systems to maintain desired properties and configurations without human intervention when subjected to dynamic, thermal, and other environmental forces. Examples are large antenna structures and flexible robotic structures. In the both cases such adaptivity would allow less massive structural members to be employed under normal loading conditions. During special circumstances when unusually large loads are encountered, temporary stiffening would allow the use of less sturdy structures, resulting in large savings in their cost, and in increasing their mobility and efficiency. Within the framework of a finite-dimensional representation of structural dynamics, the adaptivity can be implemented by the dependence of the stiffness matrix (k) upon the expected load (Q), or expected (programmed) changes in configurations, i.e., (k) = (k(t)) where the dependence upon time is programmed in advance. In order to sustain unexpected loads the adaptive structure can be provided by feedback force control, or by a parametrical stiffness control.

Zak, Michail↗
NASA NTRS1993

Remarks about massive and massless particles in supersymmetry

The internal space-time symmetry and simple supersymmetry of relativistic particles are briefly discussed in terms of the little group of the Poincare group. The little group generators in a finite-dimensional matrix representation of the N = 1 super-Poincare algebra are explicitly constructed. The supergeometry of a massive case continuously becomes that of a massless case in the infinite-momentum limit. The origin of the gage transformations associated with the massless supermultiplets becomes transparent in that limit.

Ketov, S. V.↗
NASA NTRS1982

Linear decentralized systems with special structure

Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.

Martin, C. F.↗
NASA NTRS1992

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗
NASA NTRS2010

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Barth, Timothy J.↗