Solving optimal continuous thrust rendezvous problems with generating functions

Journal of Guidance, Control, and Dynamics

Volumn 29, Issue 2, 2006, Pages 321-331

  Park, Chandeok ^a,b   Guibout, Vincent ^a,b   Scheeres, Daniel J ^a,c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b Department of Aerospace Engineering ^*  (United States)

^c AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FEEDBACK CONTROL; HAMILTONIANS; MATHEMATICAL TRANSFORMATIONS; SPACECRAFT; TRAJECTORIES;

CANONICAL TRANSFORMATION; CONTINUOUS THRUST; GENERATING FUNCTIONS; HAMILTON-JACOBI THEORY;

OPTIMAL CONTROL SYSTEMS;

EID: 33645566125     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.14580     Document Type: Article

References (20)

1. Lawden, D. F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963.
2. Billik, B. H., "Some Optimal Low-Acceleration Rendezvous Maneuvers," AIM Journal, Vol. 2, No. 3, 1964, pp. 510-516.
3. London, H. S., "Second Approximation to the Solution of the Rendezvous Equations," AIAA Journal, Vol. 1, No. 7, 1963, pp. 1691-1693.
4. Anthony, M. L., and Sasaki, F. T., "Rendezvous Problem for Nearly Circular Orbits," AIAA Journal, Vol. 3, No. 9, 1965, pp. 1066-1073.
5. Euler, E. A., "Optimal Low-Thrust Rendezvous Control," AIAA Journal, Vol. 7, No. 6, 1969, pp. 1140-1144.
6. Jezewski, D. J., and Stoolz, J. M., "A Closed-Form Solution for Minimum-Fuel, Constant-Thrust Trajectories," AIAA Journal, Vol. 8, No. 7, 1970, pp.1229-1234.
7. Marec, J., Optimal Space Trajectories, Elsevier, New York, 1979.
8. Carter, T. E., "Fuel-Optimal Maneuvers of a Spacecraft Relative to a Point in Circular Orbit," Journal of Guidance, Control, and Dynamics, Vol. 7, No. 6, 1984, pp. 710-716.
9. Carter, T., and Humi, M., "Fuel-Optimal Rendezvous Near a Point in General Keplerian Orbit," Journal of Guidance, Control, and Dynamics, Vol. 10, No. 6, 1987, pp. 567-573.
10. Humi, M., "Fuel-Optimal Rendezvous in a General Central Gravity Field," Journal of Guidance, Control, and Dynamics, Vol. 16, No. 1, 1993, pp. 215-217.
11. Carter, T. E., and Pardis, C. J., "Optimal Power-Limited Rendezvous with Upper and Lower Bounds on Thrust," Journal of Guidance, Control, and Dynamics, Vol. 19, No. 5, 1996, pp. 1124-1133.
12. Lembeck, C. A., and Prussing, J. E., "Optimal Impulsive Intercept with Low-Thrust Rendezvous Return," Journal of Guidance, Control, and Dynamics, Vol. 16, No. 3, 1993, pp. 426-433.
13. Guibout, V., and Scheeres, D. J., "Solving Relative Two Point Boundary Value Problems: Applications to Spacecraft Formation Flight Transfers," Journal of Guidance, Control, and Dynamics, Vol. 27, No. 4, 2004, pp. 693-704.
14. Guibout, V., and Scheeres, D. J., "Solving Two Point Boundary Value Problems Using Generating Functions: Theory and Applications to Astrodynamics," Astrodynamics Book Series, Elsevier (submitted for publication).
15. Park, C., and Scheeres, D. J., "Solutions of Optimal Feedback Control Problem Using Hamiltonian Dynamics and Generating Functions," Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, pp. 1222-1227.
16. Scheeres, D. J., Park, C., and Guibout, V. M., "Solving Optimal Control Problems with Generating Functions," American Astronautical Society, Paper AAS 03-575, Aug. 2003.
17. Park, C., and Scheeres, D. J., "A Generating Function for Optimal Feedback Control Laws that Satisfies the General Boundary Conditions of a System," Proceedings of the 23rd American Control Conference, 2004, pp. 679-684.
18. Park, C., and Scheeres, D. J., "Solving Optimal Feedback Control Problem with General Boundary Conditions Using Hamiltonian Dynamics and Generating Functions," Automatica (submitted for publication).
19. Greenwood, D. T., Classical Dynamics, Prentice-Hall, Englewood Cliffs, NJ, 1977, pp. 187-271.
20. Bryson, A. E., and Ho, Y., Applied Optimal Control, Taylor and Francis, Bristol, PA, 1975, pp. 148-176.