Solving optimal control problems using hp-version finite elements in time

Journal of Guidance, Control, and Dynamics

Volumn 23, Issue 1, 2000, Pages 86-94

  Warner, Michael S ^a,b   Hodges, Dewey H ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b USAF   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; NONLINEAR SYSTEMS; PROBLEM SOLVING;

NONLINEAR SYSTEM DYNAMICS;

OPTIMAL CONTROL SYSTEMS;

EID: 0033879119     PISSN: 07315090     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.4490     Document Type: Article

References (18)

1. Hodges, D. H., and Bless, R. R., "A Weak Hamiltonian Finite Element Formulation for Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 14, No. 1, 1991, pp. 148-156.
2. Bless, R. R., "Time-Domain Finite Elements in Optimal Control with Application to Launch Vehicle Guidance," NASA TR CR 4376, May 1991.
3. Bless, R. R., and Hodges, D. H., "Finite Element Solution of Optimal Control Problems with State-Control Inequality Constraints," Journal of Guidance, Control, and Dynamics, Vol. 15, No. 4, 1992, pp. 1029-1032.
4. Bless, R. R., Hodges, D. H., and Seywald, H., "A Finite Element Method for the Solution of State-Constrained Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 18, No. 5, 1995, pp. 1036-1043.
5. Johnson, M. G., Jr., Haskins, G. T., and Hodges, D. H., "Real Time Missile Guidance System," U.S. Patent 5,435,503, July 1995.
6. Bryson, A. E., Jr., and Ho, Y-C., Applied Optimal Control, Blaisdell, Waltham, MA, 1975, Chaps. 2 and 3.
7. Warner, M. S., and Hodges, D. H., "Treatment of Control Constraints as Zeroth-Order State Constraints in Finite Element Solution of Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 22, No. 2, 1999, pp. 358-360.
8. Gelfand, I. M., and Fomin, S. V., Calculus of Variations, Prentice-Hall, Upper Saddle River, NJ, 1963, Chap. 2.
9. Hodges, D. H., and Hou, L.-J., "Shape Functions for Mixed p-version Finite Elements in the Time Domain," Journal of Sound and Vibration, Vol. 145, No. 2, 1991, pp. 169-178.
10. Abramowitz, M., and Stegun, I. (eds.), Handbook of Mathematical Functions, National Bureau of Standards, Washington, DC, 1970.
11. Duff, I. S., Harwell Subroutine Library, Computer Science and System Div., Harwell Lab., Oxfordshire, England, UK, Feb. 1988.
12. MACSYMA Reference Manual, Symbolics, Inc., Burlington, MA, 1988.
13. Maple V Mathematics Programming Guide, Springer-Verlag, Waterloo, Belgium, 1995.
14. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., Numerical Recipes: The Art of Scientific Computing, Cambridge Univ. Press, Cambridge, England, UK, 1986, Chap. 16.
15. Estep, D. J., Hodges, D. H., and Warner, M. S., "Computational Error Estimation for Finite Element Solution of Missile Trajectory Optimization Problems," SIAM Journal on Scientific Computing (to be published).
16. Hodges, D. H., and Johnson, M. G., Jr., "Control Variables for Finite Element Solution of Missile Trajectory Optimization," Journal of Guidance, Control, and Dynamics, Vol. 18, No. 5, 1995, pp. 1208-1211.
17. Hodges, D. H., "Finite Rotation and Nonlinear Beam Kinematics," Vertica, Vol. 11, No. 1/2, 1987, pp. 297-307.
18. Battin, R. H., An Introduction to the Mathematics and Methods of Astrodynamics, AIAA, Washington, DC, 1987, Sec. 10.4.