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Results for “RECURSION FORMULA”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Closed-form recursive formula for an optimal tracker with terminal constraints

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. Two examples are given to illustrate the validity and usefulness of the formulations.

Juang, J.-N.↗
NASA NTRS1986

Closed-form recursive formula for an optimal tracker with terminal constraints

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.

Juang, J. N.↗
NASA NTRS1973

Recursive formulas for the partial fraction expansion of a rational function with multiple poles.

The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.

Chang, F.-C.↗
NASA NTRS1975

Weight minimization of structures for fixed flutter speed via an optimality criterion

A rigorous optimality criterion is derived and a hybrid weight-reduction algorithm developed for the weight minimization of lifting surfaces with a constraint on flutter speed. The weight-reduction algorithm incorporates a simple recursion formula derived from the optimality criterion. Monotonic weight reduction is accomplished by dynamically adjusting a parameter in the recursion formula so as to achieve a predetermined weight decrease. The algorithm thus combines the simplicity of optimality-criterion methods with the convergence characteristics of mathematical-programming methods. The imposition of the flutter constraint is simplified by forcing to zero the imaginary part of the flutter eigenvalue, with the airspeed fixed. Four examples are discussed. The results suggest that significant improvements in efficiency are possible, in comparison with techniques based purely on mathematical programming.

Segenreich, S. A.↗
NASA NTRS1985

Multivariate Spline Algorithms for CAGD

Two special polyhedra present themselves for the definition of B-splines: a simplex S and a box or parallelepiped B, where the edges of S project into an irregular grid, while the edges of B project into the edges of a regular grid. More general splines may be found by forming linear combinations of these B-splines, where the three-dimensional coefficients are called the spline control points. Univariate splines are simplex splines, where s = 1, whereas splines over a regular triangular grid are box splines, where s = 2. Two simple facts render the development of the construction of B-splines: (1) any face of a simplex or a box is again a simplex or box but of lower dimension; and (2) any simplex or box can be easily subdivided into smaller simplices or boxes. The first fact gives a geometric approach to Mansfield-like recursion formulas that express a B-spline in B-splines of lower order, where the coefficients depend on x. By repeated recursion, the B-spline will be expressed as B-splines of order 1; i.e., piecewise constants. In the case of a simplex spline, the second fact gives a so-called insertion algorithm that constructs the new control points if an additional knot is inserted.

Boehm, W.↗
NASA NTRS1989

An improved algorithm for optimum structural design with multiple frequency constraints

An optimality criterion (OC) method for minimum-weight design of structures having multiple constraints on natural frequencies is presented. In this work a new resizing strategy is developed based on relaxation techniques. A computationally adaptive control parameter is used in conjunction with existing OC recursive formulae to promote convergence of optimum structural designs. Some considerations regarding the coupling of the modified Aitken accelerator with the OC method are discussed. Improved and rapidly converged minimum-weight designs are obtained when using an under-relaxed recursive scheme combined with the modified Aitken accelerator.

Mcgee, Oliver G.↗