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Powers, W. F.

Publications and source records attributed to Powers, W. F..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Optimal low-thrust takeoff from an orbit about an oblate planet

Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, and the nondimensional thrust acceleration are the same order of magnitude. By means of a two-variable asymptotic expansion technique, a near optimal control program is generated and the first-order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.

Jacobson, R. A.↗
NASA NTRS1976

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.

Edge, E. R.↗
NASA NTRS1976

Astrodynamics 1975; Conference, Nassau, Bahamas, July 28-30, 1975, Technical Papers

Articles are grouped under four headings: (1) dynamics and control of satellites; (2) satellite mission analysis; (3) Aeros-B and Symphonie satellite engineering problems; (4) optimization and control techniques applied to solar space heating and cooling of buildings. Topics covered include: communications and earth survey satellite systems, a system of two counter-orbiting satellites measuring GRT-predicted nodal drag, statistical mechanics studies of the spatial density function of orbiting space junk, attitude control of satellites, nutation dampers, low thrust inertial guidance and ascent inertial guidance, a shuttle-launched multi-comet intercept mission, preflight and in-flight analysis of the Atmosphere Explorer (AE-C) satellite, and launch-encounter strategy for the Mariner 1977 Jupiter-Saturn mission. Individual items are announced in this issue.

Powers, W. F.↗
NASA NTRS1974

Neighboring optimal guidance theory and computer program

Developments of the linear quadratic optimal control problem are discussed. The theory is applicable to the development of neighboring optimal feedback guidance gains, and is useful as a tool for synthesizing feedback control laws. A computer program which requires only the pertinent matrices of the linear quadratic problem is described.

Powers, W. F.↗
NASA NTRS1974

Shuttle ascent trajectory optimization with function space quasi-Newton techniques

A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.

Edge, E. R.↗
NASA NTRS1973

Techniques for shuttle trajectory optimization

The application of recently developed function-space Davidon-type techniques to the shuttle ascent trajectory optimization problem is discussed along with an investigation of the recently developed PRAXIS algorithm for parameter optimization. At the outset of this analysis, the major deficiency of the function-space algorithms was their potential storage problems. Since most previous analyses of the methods were with relatively low-dimension problems, no storage problems were encountered. However, in shuttle trajectory optimization, storage is a problem, and this problem was handled efficiently. Topics discussed include: the shuttle ascent model and the development of the particular optimization equations; the function-space algorithms; the operation of the algorithm and typical simulations; variable final-time problem considerations; and a modification of Powell's algorithm.

Edge, E. R.↗
NASA NTRS1973

Numerical integration routines for near-earth operations

Two general purpose numerical integration schemes were built into the NASA-JSC computer system. The state-of-the-art of numerical integration, the particular integrators built into the JSC computer system, and the use of the new integration packages are described. Background information about numerical integration and the variable-order, variable-stepsize Adams numerical integration technique is discussed. Results concerning the PEACE parameter optimization program are given along with recommendations and conclusions.

Powers, W. F.↗
NASA NTRS1973

Function space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function space algorithms, Davidon and projected gradient, are modified so that they may handle directly control variable inequality constraints. A third quasi-Newton type algorithm developed by C. G. Broyden is extended to optimal control problems. The Broyden algorithm is further modified so that it also may handle directly control variable inequality constraints. These methods along with a pure gradient and two conjugate gradient algorithms are simulated on three relatively simple yet representative bounded control problems, two of which have singular subarcs. Overall the Broyden algorithm was found to be superior. The most notable result of the study was the clear superiority of the Broyden and Davidon algorithms in producing a sharp interior control subarc.

Edge, E. R.↗
NASA NTRS1972

Near-earth orbital guidance and remote sensing

The curriculum of a short course in remote sensing and parameter optimization is presented. The subjects discussed are: (1) basics of remote sensing and the user community, (2) multivariant spectral analysis, (3) advanced mathematics and physics of remote sensing, (4) the atmospheric environment, (5) imaging sensing, and (6)nonimaging sensing. Mathematical models of optimization techniques are developed.

Powers, W. F.↗
NASA NTRS1972

Asymptotic solution to the problem of optimal low-thrust energy increase.

Consideration of the problem of optimal ascent from an initial circular planetary orbit to some specified final energy level by a spacecraft equipped with a low-thrust engine. Optimal is defined as minimum time. An accurate small parameter perturbation solution is presented, and the optimal trajectory is analyzed and compared with a tangential thrust trajectory.

Jacobson, R. A.↗
NASA NTRS1972

Iterative explicit guidance for low thrust spacecraft.

A retargeting procedure is developed for use as a nonlinear low thrust guidance scheme. The selection of a control program composed of a sequence of inertially fixed thrust-acceleration vectors permits all trajectory computations to be made with closed form expressions, and allows the controls to be represented by constant parameters, thrust-acceleration vectors and thrusting times. By requiring each trajectory to be time optimal, the guidance problem is transformed into a parameter optimization problem which is solved by the conjugate gradient method. The scheme is applied to a low thrust capture mission, and the results of computer simulations are presented.

Jacobson, R. A.↗
NASA NTRS1972

Conjugate gradient optimization programs for shuttle reentry

Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems.

Powers, W. F.↗