SEARCH · Engineering Papers

Results for “linear systems”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,153 records · Page 64

All sources NASA NTRS DOE OSTI

NASA NTRS1987

Order reduction in linear state estimation under performance constraints

The design and analysis of minimal-order state estimators for possibly time-varying linear systems, under constraints on the maximal allowable mean-square error, are considered. A global lower bound on the optimal error is derived, along with a lower bound on the minimal estimator order, needed for meeting the performance constraint. The ideal reduced-order estimator which satisfies the lower bound is derived, along with conditions for its realizability. When the ideal estimator is not realizable, its structure forms a suboptimal estimator, which maintains, in some sense, a local optimality property and is called the pseudoideal estimator. The mean-square error of the pseudoideal estimator defines upper bounds on the optimal error and on the estimator order needed for meeting the performance constraint. The lower and the upper bounds on the order define a reduced search set for the design problem. When the distance between the ideal and the pseudoideal estimators is sufficiently small in a certain numerical sense, the pseudoideal estimator may be considered optimal for practical purposes.

Baram, Yoram↗

NASA NTRS1987

Mean-square-error bounds for reduced-order linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Liapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗

NASA NTRS1988

Derivation and definition of a linear aircraft model

A linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth is derived and defined. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.

Duke, Eugene L.↗

NASA NTRS1988

Totally parallel multilevel algorithms

Four totally parallel algorithms for the solution of a sparse linear system have common characteristics which become quite apparent when they are implemented on a highly parallel hypercube such as the CM2. These four algorithms are Parallel Superconvergent Multigrid (PSMG) of Frederickson and McBryan, Robust Multigrid (RMG) of Hackbusch, the FFT based Spectral Algorithm, and Parallel Cyclic Reduction. In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which are referred to as TPMA. In certain cases the spectral radius of TPMA is zero, and it is recognized to be a direct algorithm. In many other cases the spectral radius, although not zero, is small enough that a single iteration per timestep keeps the local error within the required tolerance.

Frederickson, Paul O.↗

NASA NTRS1988

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Freund, Roland↗

NASA NTRS1987

Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

Bayard, D. S.↗

NASA NTRS1988

Probabilistic methods for structural response analysis

This paper addresses current work to develop probabilistic structural analysis methods for integration with a specially developed probabilistic finite element code. The goal is to establish distribution functions for the structural responses of stochastic structures under uncertain loadings. Several probabilistic analysis methods are proposed covering efficient structural probabilistic analysis methods, correlated random variables, and response of linear system under stationary random loading.

Wu, Y.-T.↗

NASA NTRS1988

IMF control of geomagnetic activity

Recent work on the IMF control of geomagnetic activity is reviewed. The goal is to quantitatively express the temporal relation between the solar wind input and the ionospheric output from the magnetospheric system. Linear prediction filtering was used which treats the magnetosphere as a black box characterized by an impulse response. It is shown that an average impulse response can account for only about 40 percent of the variance in the AL index.

Mcpherron, R. L.↗

NASA NTRS1990

Output Control Using Feedforward And Cascade Controllers

Report presents theoretical study of open-loop control elements in single-input, single-output linear system. Focus on output-control (servomechanism) problem, in which objective is to find control scheme that causes output to track certain command inputs and to reject certain disturbance inputs in steady state. Report closes with brief discussion of characteristics and relative merits of feedforward, cascade, and feedback controllers and combinations thereof.

Seraji, Homayoun↗

NASA NTRS1990

Polynomial Compensation, Inversion, And Approximation

New criterion introduced for design of discrete-time compensator. Method devised for polynomial compensation, inversion, and approximation of discrete-time linear systems. Involves quadratic measure of difference between response of compensated system and desired response. Impulse response of compensated system improves as degree of polynomial increases. Compensator emphasizes matching of large initial response. Compensators used in variety of applications, including navigation systems for spacecraft, aircraft, ships, and automated manufacturing equipment.

Baram, Yoram↗

NASA NTRS1989

Krylov methods preconditioned with incompletely factored matrices on the CM-2

The performance is measured of the components of the key interative kernel of a preconditioned Krylov space interative linear system solver. In some sense, these numbers can be regarded as best case timings for these kernels. Sweeps were timed over meshes, sparse triangular solves, and inner products on a large 3-D model problem over a cube shaped domain discretized with a seven point template. The performance of the CM-2 is highly dependent on the use of very specialized programs. These programs mapped a regular problem domain onto the processor topology in a careful manner and used the optimized local NEWS communications network. The rather dramatic deterioration in performance was documented when these ideal conditions no longer apply. A synthetic workload generator was developed to produce and solve a parameterized family of increasingly irregular problems.

Berryman, Harry↗

NASA NTRS1990

Parallel algorithms for boundary value problems

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Lin, Avi↗

NASA NTRS1989

A survey on the structured singular value

The structured singular value, U, is an important linear algebra tool to study a class of matrix perturbation problems. It is useful for analyzing the robustness of stability and performance of uncertain, (nominally) linear systems. Computation of (M) is difficult, and usually, upper and lower bounds are all that can be reliably computed. Upper bounds give conservative estimates of the sizes of allowable perturbations. The maximum singular value of a matrix M is an upper bound for (M). As an upper bound, it can be improved by finding a transformations to the data (i.e. M) which do not change the structured singular value, but do reduce the maximum singular value. Typically, upper bound algorithms involve searches over sets of transformations to yield the tightest bound. Lower bound algorithms are intelligent searches for minimum-norm solutions to multivariable polynomial equations, and are based on various optimality conditions that hold at the global (and, unfortunately, some local) minima. The current methods to compute both of these types of bounds are reviewed. Theoretical justification and extensive numerical experience with the various algorithms are covered.

Packard, Andy↗

NASA NTRS1989

Parallel conjugate gradient algorithms for manipulator dynamic simulation

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

Fijany, Amir↗

NASA NTRS1989

On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Gallopoulos, E.↗

NASA NTRS1990

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

Decker, Naomi H.↗

NASA NTRS1989

Portable Dextrous Force Feedback Master for robot telemanipulation (PDMFF)

A major drawback of open loop masters is a lack of force feedback, limiting their ability to perform complex tasks such as assembly and repair. Researchers present a simple dextrous force feedback master for computer assisted telemanipulation. The device is compact, portable and can be held in the operator hand, without the need for a special joystick or console. The system is capable of both position feed forward and force feedback, using electronic position sensors and a pneumatic micro-actuator. The level of forces exercised by the pneumatic actuator is such that near rigidity may be attained. Experimental results showing good system linearity and small time lag are given.

Burdea, Grigore C.↗

NASA NTRS1989

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.

Gallopoulos, E.↗