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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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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Childs, A. G.↗
NASA NTRS1972

A shielding application of perturbation theory to determine changes in neutron and gamma doses due to changes in shield layers

The perturbation theory for fixed sources was applied to radiation shielding problems to determine changes in neutron and gamma ray doses due to changes in various shield layers. For a given source and detector position the perturbation method enables dose derivatives due to all layer changes to be determined from one forward and one inhomogeneous adjoint calculation. The direct approach requires two forward calculations for the derivative due to a single layer change. Hence, the perturbation method for obtaining dose derivatives permits an appreciable savings in computation for a multilayered shield. For an illustrative problem, a comparison was made of the fractional change in the dose per unit change in the thickness of each shield layer as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.

Fieno, D.↗
NASA NTRS1972

An Optimization study on a hybrid computer

The maximum principle is applied to minimum-time optimal-control problems, and an optimization algorithm is presented which can be implemented on a hybrid computer. The state and adjoint equations are set up on ASTRAC 2, a high-speed analog computer capable of 1000 differential equation solutions per second. The optimization algorithm is implemented on a PDP-9, an 18-bit, digital computer. The optimization scheme has global and local search phases and uses a vector optimization criterion. Second and third-order bang-bang control systems are studied as examples.

Gonzalez, R. S.↗
NASA NTRS1971

Optimal startup control of a jacketed tubular reactor.

The optimal startup policy of a jacketed tubular reactor, in which a first-order, reversible, exothermic reaction takes place, is presented. A distributed maximum principle is presented for determining weak necessary conditions for optimality of a diffusional distributed parameter system. A numerical technique is developed for practical implementation of the distributed maximum principle. This involves the sequential solution of the state and adjoint equations, in conjunction with a functional gradient technique for iteratively improving the control function.

Hahn, D. R.↗
NASA NTRS1972

Surface roughness effects on equilibrium temperature.

An analysis is presented for evaluation of equilibrium temperature distribution on radiatively adiabatic, adjoint planes which are uniformly irradiated by a collimated solar flux. The analysis employs a semigrey spectral model. Radiation properties for surface emitted radiation are obtained from the expressions of electromagnetic theory for smooth surfaces. Rough surface properties for solar radiation are given by the Beckmann bidirectional reflectance model. Numerical solutions to the governing equations yield equilibrium temperature distributions for a range of the influencing parameters. Surface roughness has little influence on equilibrium temperature for materials with high values for solar absorptance. However, for low or intermediate values of solar absorptance, roughness effects on the spatial distribution of reflected solar radiation can significantly alter equilibrium temperature particularly at surface elements where radiant interaction is small.

Houchens, A. F.↗
NASA NTRS1972

Some impulsive rendezvous trajectories and their possible optimality.

Two- and three-impulse trajectories are investigated for fixed-time, fixed-angle rendezvous between vacant circular coplanar orbits, for trip angles less than, or equal to 2 pi in magnitude. For two-impulse trajectories, general features of the characteristic velocity function are outlined. Parameters of the intermediate orbit are reviewed. Attention is given to limiting cases. Computation of the adjoint system helps to define the domain of possible optimality foajectories: it is a closed domain in the trip time, trip angle plane. Waiting periods on terminal orbits are considered. The domain of possible optimality is defined using Lawden's primer vrtory. This domain extends to infinity if the radius ratio of terminal orbits is less than 15.6. Three-impulse trajectories are tried in cases where two-impulse trajectories, with or without cost, have been found nonoptimal. Improvements on the characteristic velocity are thus obtained.

Peltier, J. P.↗
NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. I.

Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.

Baxley, J. V.↗
NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. II.

Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.

Baxley, J. V.↗