Multiple-subarc gradient-restoration algorithm, part 1: Algorithm structure

Journal of Optimization Theory and Applications

Volumn 116, Issue 1, 2003, Pages 1-17

  Miele, A ^a   Wang, T ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

Algorithms; multiple subarc algorithms; multistage launch vehicle design; sequential gradient restoration algorithms; single subarc algorithms

Indexed keywords

BOUNDARY VALUE PROBLEMS; EARTH (PLANET); INTERFACE STATES; OPTIMAL CONTROL SYSTEMS; ORBITS; RESTORATION; ROCKETS; SPACE FLIGHT; TIME DOMAIN ANALYSIS;

LAUNCH VEHICLE DESIGN; MULTIPLE-SUBARC ALGORITHM; MULTIPLE-SUBARC GRADIENT-RESTORATION ALGORITHMS; MULTISTAGE LAUNCH VEHICLE DESIGN; MULTISTAGE LAUNCH VEHICLES; RESTORATION ALGORITHM; SEQUENTIAL GRADIENT-RESTORATION ALGORITHM; SINGLE-SUBARC ALGORITHM; SUB-ARC;

EFFICIENCY;

EID: 0037270416     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022114117273     Document Type: Article

References (25)

1. MIELE, A., and WANG, T., Multiple-Subarc Sequential Gradient-Restoration Algorithm and Application to Launch Vehicle Design, Paper Presented at the 6th SIMAI National Congress, Chia Laguna, Cagliari, Italy, 27-31 May 2002.
2. MIELE, A., and WANG, T., Multiple-Subarc Gradient-Restoration Algorithm, Part 2: Application to a Multistage Launch Vehicle Design, Journal of Optimization Theory and Applications, Vol. 116, No. 1, pp. 19-39, 2003.
3. HARGRAVES, C. R., and PARIS, S. W., Direct Trajectory Optimization Using Nonlinear Programming and Collocation, Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, pp. 338-342, 1987.
4. BETTS, J. T., and CRAMER, E. J., Application of Direct Transcription to Commercial Aircraft Trajectory Optimization, Journal of Guidance, Control, and Dynamics, Vol. 18, No. 1, pp. 151-159, 1995.
5. KREIM, H., KUGELMANN, B., PESCH, H. J., and BREITNER, M. H., Minimizing the Maximum Heating of a Reentering Space Shuttle: An Optimal Control Problem with Multiple Control Constraints, Optimal Control Applications and Methods, Vol. 17, No. 1, pp. 45-69, 1996.
6. BETTS, J. T., Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, pp. 193-207, 1998.
7. HERMAN, A. L., and SPENCER, D. B., Optimal Low-Thrust Earth-Orbit Transfers Using Higher-Order Collocation Methods, Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, pp. 40-47, 2002.
8. MIELE, A., PRITCHARD, R. E., and DAMOULAKIS, J. N., Sequential Gradient-Restoration Algorithm for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 5, No. 4, pp. 235-282, 1970.
9. MIELE, A., DAMOULAKIS, J. N., CLOUTIER, J. R., and TIETZE, J. L., Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints, Journal of Optimization Theory and Applications, Vol. 13, No. 2, pp. 218-255, 1974.
10. MIELE, A., Recent Advances in Gradient Algorithms for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 17, Nos. 5-6, pp. 361-430, 1975.
11. GONZALEZ, S., and MIELE, A., Sequential Gradient-Restoration Algorithm for Optimal Control Problems with General Boundary Conditions, Journal of Optimization Theory and Applications, Vol. 26, No. 3, pp. 395-425, 1978.
12. MIELE, A., CLOUTIER, J. R., MOHANTY, B. P., and WU, A. K., Sequential Conjugate Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints, Parts 1 and 2, International Journal of Control, Vol. 29, No. 2, pp. 189-211 and pp. 213-234, 1979.
13. MIELE, A., Gradient Algorithms for the Optimization of Dynamic Systems, Control and Dynamic Systems, Advances in Theory and Application, Edited by C. T. Leondes, Academic Press, New York, NY, Vol. 16, pp. 1-52, 1980.
14. MIELE, A., and WANG, T., Primal-Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 1: Basic Problem, Integral Methods in Science and Engineering, Edited by F. R. Payne et al., Hemisphere Publishing Corporation, Washington, DC, pp. 577-607, 1986.
15. MIELE, A., and WANG, T., Primal-Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 2: General Problem, Journal of Mathematical Analysis and Applications, Vol. 119, Nos. 1-2, pp. 21-54, 1986.
16. MIELE, A., WANG, T., and BASAPUR, V. K., Primal and Dual Formulations of Sequential Gradient-Restoration Algorithms for Trajectory Optimization Problems, Acta Astronautica, Vol. 13, No. 8, pp. 491-505, 1986.
17. RISHIKOF, B. H., MCCORMICK, B. R., PRITCHARD, R. E., and SPONAUGLE, S. J., SEGRAM: A Practical and Versatile Tool for Spacecraft Trajectory Optimization, Acta Astronautica, Vol. 26, Nos. 8-10, pp. 599-609, 1992.
18. MIELE, A., WANG, T., and MELVIN, W. W., Optimal Take-Off Trajectories in the Presence of Windshear, Journal of Optimization Theory and Applications, Vol. 49, No. 1, pp. 1-45, 1986.
19. MIELE, A., and WANG, T., Optimal Transfers from an Earth Orbit to a Mars Orbit, Acta Astronautica, Vol. 45, No. 3, pp. 119-133, 1999.
20. MIELE, A., and MANCUSO, S., Optimal Trajectories for Earth-Moon-Earth Flight, Acta Astronautica, Vol. 49, No. 11, pp. 59-71, 2001.
21. MIELE, A., and WANG, T., Nominal Trajectories for the Aeroassisted Flight Experiment, Journal of the Astronautical Sciences, Vol. 41, No. 2, pp. 139-163, 1993.
22. MIELE, A., and MANCUSO, S., Optimal Ascent Trajectories and Feasibility of Next-Generation Orbital Spacecraft, Journal of Optimization Theory and Applications, Vol. 97, No. 3, pp. 519-550, 1998.
23. MIELE, A., and MANCUSO, S., On Feasibility of Suborbital and Orbital Rocket-Powered Spacecraft, Memorie della Accademia delle Scienze di Torino, Vol. 24, pp. 83-109, 2000.
24. MIELE, A., WANG, T., and MANCUSO, S., Assessment of Launch Vehicle Advances to Enable Human Mars Excursions, Acta Astronautica, Vol. 49, No. 11, pp. 563-580, 2001.
25. HENNIG, G., and MIELE, A., Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Bounded State, Journal of Optimization Theory and Applications, Vol. 12, No. 1, pp. 61-98, 1973.