A Comparison of the Gradient and Newton-Raphson Techniques for Reentry Trajectory Optimization
Title | A Comparison of the Gradient and Newton-Raphson Techniques for Reentry Trajectory Optimization PDF eBook |
Author | William E. Henson |
Publisher | |
Pages | 172 |
Release | 1972 |
Genre | |
ISBN |
The report contains a two-dimensional optimization analysis of reentry trajectories for minimization of space vehicle heating and maximization of terminal range, conducted for a lifting body reentry vehicle with a maximum lift-to-drag of three. Based on this analysis there appears to be a conflict between heat minimization and range maximization in that a high angle-of-attack is required to minimize the heating rate and a lower angle-of-attack is required to maximize range. Two optimization techniques were compared, a Newton-Raphson method and a steepest-descent gradient method. A modification of the gradient technique, which was based upon the variational Hamiltonian, was applied after convergence to a near-optimal solution, resulting in an improved control profile. (Author).
A Comparison of the Gradient and Newton-Raphson Techniques for Reentry Trajectory Optimization
Title | A Comparison of the Gradient and Newton-Raphson Techniques for Reentry Trajectory Optimization PDF eBook |
Author | William E. Henson (MAJ, USAF.) |
Publisher | |
Pages | 320 |
Release | 1972 |
Genre | Space vehicles |
ISBN |
Scientific and Technical Aerospace Reports
Title | Scientific and Technical Aerospace Reports PDF eBook |
Author | |
Publisher | |
Pages | 1102 |
Release | 1973 |
Genre | Aeronautics |
ISBN |
STAR
Title | STAR PDF eBook |
Author | |
Publisher | |
Pages | 892 |
Release | 1973 |
Genre | Aeronautics |
ISBN |
Masters Theses and Doctoral Dissertations in the Pure and Applied Sciences Accepted by Colleges and Universities of the United States
Title | Masters Theses and Doctoral Dissertations in the Pure and Applied Sciences Accepted by Colleges and Universities of the United States PDF eBook |
Author | |
Publisher | |
Pages | 544 |
Release | 1971 |
Genre | Chemistry |
ISBN |
Master's Theses and Doctoral Dissertations in the Pure and Applied Sciences
Title | Master's Theses and Doctoral Dissertations in the Pure and Applied Sciences PDF eBook |
Author | |
Publisher | |
Pages | 194 |
Release | 1973 |
Genre | Dissertations, Academic |
ISBN |
A Combined Newton-Raphson and Gradient Parameter Correction Technique for Solution of Optimal-control Problems
Title | A Combined Newton-Raphson and Gradient Parameter Correction Technique for Solution of Optimal-control Problems PDF eBook |
Author | Ernest S. Armstrong |
Publisher | |
Pages | 76 |
Release | 1968 |
Genre | Boundary value problems |
ISBN |
A parameter correction technique is developed to solve a boundary-value problem which frequently occurs in optimal-control theory. It is assumed that an indirect optimal-control method has been applied to a controllable dynamic system with a two-point boundary-value problem resulting such that the boundary conditions take the form of a set of unknown parameters to be determined to meet an equal number of terminal conditions. The optimal-control law is a piecewise continuous function with discontinuities occurring only at the zeros of certain continuous functions. A procedure is developed to improve upon an assumed set of parameters so that, by repetitive use of a correction formula, a monotonic decreasing sequence of values of a positive definitive function that measures the terminal errors is produced. The direction of the correction vector is found to lie between the directions given by the gradient and the Newton-Raphson procedures. Integral equations are derived for influence matrices that describe the effect of a change in the parameters on the terminal conditions. The procedure is successfully applied to the determination of both planar and nonplanar fuel-optimal trajectories for a space vehicle which is launched from the surface of the moon and required to rendezvous with a space vehicle in a circular orbit.