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Results for “Sylvester equation”

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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7 records

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

Constrained Field Construction Using Bernstein Polynomial Derived Operators

This method recasts the mass-conservation equation as a Sylvester equation employing high-order derivative operators derived from modified Bernstein polynomial expansions. Given prescribed velocity fields, the algorithm yields a constrained, least-squared solution for the associated density field. To demonstrate the practical utility of this methodology, it is applied to a computationally-derived two-dimensional isolator dataset. This reconstruction method is envisioned to be used in conjunction with diagnostic techniques to aid in the quantification of isolator flow fields, since obtaining highly characterized datasets within this engine component is exceedingly difficult.

Isolator↗

NASA NTRSDate not supplied

Field Reconstruction from PIV Measurements Employing Bernstein Polynomial Derived Operators

A fluid-dynamic reconstruction algorithm is presented that generates a least-squares best-fit, two-dimensional density field from a prespecified two-dimensional velocity field. This method recasts the mass-conservation equation as a modified Sylvester equation employing high-order operators derived from modified Bernstein polynomial expansions. To demonstrate its practical utility, this analytic methodology is applied to two canonical cases and a Particle Image Velocimetry dataset obtained from a Mach-2, mechanically back-pressured, isolator experiment. This methodology is envisioned to be used in conjunction with hypersonic-diagnostic techniques to aid in the quantification of isolator flow fields. However, also note that this reconstruction technique is well suited to other applications relevant to fluid dynamics, such as obtaining three-dimensional flow field reconstructions.

Bernstein Polynomials↗

NASA NTRS2017

Performance Optimizing Adaptive Control with Time-Varying Reference Model Modification

This paper presents a new adaptive control approach that involves a performance optimization objective. The control synthesis involves the design of a performance optimizing adaptive controller from a subset of control inputs. The resulting effect of the performance optimizing adaptive controller is to modify the initial reference model into a time-varying reference model which satisfies the performance optimization requirement obtained from an optimal control problem. The time-varying reference model modification is accomplished by the real-time solutions of the time-varying Riccati and Sylvester equations coupled with the least-squares parameter estimation of the sensitivities of the performance metric. The effectiveness of the proposed method is demonstrated by an application of maneuver load alleviation control for a flexible aircraft.

Adaptive Control↗

NASA NTRS2018

Time-Varying Modification of Reference Model for Adaptive Control with Performance Optimization

This paper presents a new adaptive control ap- proach that involves a performance optimization objective. The control synthesis involves the design of a performance optimizing adaptive controller from a subset of control inputs. The resulting effect of the performance optimizing adaptive controller is to modify the initial reference model into a time-varying reference model which satisfies the performance optimization requirement obtained from an optimal control problem. The time-varying reference model modification is accomplished by the real-time solutions of the time-varying Riccati and Sylvester equations coupled with the least-squares parameter estimation of the sen- sitivities of the performance metric. The effectiveness of the proposed method is demonstrated by an application of maneuver load alleviation control for a flexible aircraft.

Adaptive Control↗

NASA NTRSDate not supplied

Time-Varying Reference Model Modification of Adaptive Control with Multi-Objective Performance Optimization

This paper presents an adaptive control approach that modifies a reference model in order to satisfy a multi-objective optimization of two performance signals: a linear signal and a quadratic signal. The time varying reference model modification is accomplished by the real-time solutions of the time-varying Riccati and Sylvester equations coupled with the least-squares parameter estimation of the sensitivities of the performance signals to be minimized. The effectiveness of the proposed method is to be demonstrated by a flight control application of maneuver load alleviation and drag minimization.

Adaptive Control↗

NASA NTRS1989

Overview of Krylov subspace methods with applications to control problems

An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.

Saad, Youcef↗

NASA NTRS1992

The algebraic decoding of the (41, 21, 9) quadratic residue code

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

Reed, Irving S.↗