Direct trajectory optimization by a Chebyshev pseudospectral method

Proceedings of the American Control Conference

Volumn 6, Issue , 2000, Pages 3860-3864

  Fahroo, Fariba ^a   Ross, I Michael ^a  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEBYSHEV-PSEUDOSPECTRAL METHOD; COLLOCATION METHOD; EXPANSION COEFFICIENTS; NONLINEAR PROGRAMMING PROBLEM; NUMERICAL EXAMPLE; OPTIMAL CONTROL PROBLEM; STATE AND CONTROL CONSTRAINTS; TRAJECTORY OPTIMIZATION;

POLYNOMIAL APPROXIMATION; APPROXIMATION THEORY; CONSTRAINT THEORY; CONTROL SYSTEM ANALYSIS; LAGRANGE MULTIPLIERS; NONLINEAR PROGRAMMING; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

OPTIMAL CONTROL SYSTEMS;

CHEBYSHEV PSEUDOSPECTRAL METHOD; CHEBYSHEV-GAUSS-LOBATTO POINTS; LAGRANGE POLYNOMIAL APPROXIMATIONS; TRAJECTORY OPTIMIZATION;

EID: 0034539833     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2000.876945     Document Type: Conference Paper

References (13)

1. Betts, J. T., " Survey of Numerical Methods for Trajectory Optimization," Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998, pp. 193-207.
2. Canuto, C., Hussaini, M.Y., Quarteroni, A., and Zang, T.A., Spectral Methods in Fluid Dynamics, Springer Verlag, New York, 1988.
3. Conway B.A. and Larson, K. M., "Collocation Versus Differential Inclusion in Direct Optimization," Journal of Guidance. Control, and Dynamics, Vol. 21, NO. 5, 1998, pp. 780-785.
4. Elnagar, J., Kazemi, M.A. and Razzaghi, M., " The Pseudospectral Legendre Method for Discretizing Optimal Control Problem,'' IEEE 'Pransactions on Automatic Control, Vol. 40, No. 10, 1995, pp. 1793-1796.
5. Fahroo, F., and Ross, I. M., " Computational Optimal Control by Spectral Collocation with differential Inclusion," Proceedings of Flight Mechanics Symposium, Goddard Space Flight Center, May 1999, NASA/CP-1999-209235.
6. Fahroo, F., and Ross, I. M., " Costate Estimation by a Legendre Pseudospectral Method," accepted for publication in the Journal of Guidance, Control, and Dynamics.
7. Gottlieb, D., Hussaini, M.Y., and Orszag, S. A., "Theory and Applications of Spectral Methods," in Spectral Methods for PDE's, Philadelphia, PA: SIAM, 1984.
8. 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, 1987, pp. 338-342.
9. Herman, A. H., and Conway B.A., " Direct Optimization Using Collocation Based on Hight-Order Gauss-Lobatto Quadrature Rules," Journal of Guidance. Control, and Dynamics, Vol. 19, No. 3, 1996, pp. 592-599.
10. Hull, D. G., " Conversion of Optimal Control Problems into Parameter Optimization Problems," Journal of Guidance, Control, and Dynamics, Vol. 20, NO. 1, 1997, pp. 57-60.
11. Knowles, G., An Introduction to Applied Optimal Control, Academic Press Inc., New York, 1981.
12. Vlassenbroeck, J. and Van Doreen, R., " A Chebyshev Technique for Solving Nonlinear Optimal Control Problems," IEEE Trans. Automat. Contr. Vol. 33, 1988, pp. 333-340.
13. von Stryk, O., "Numerical Solution of Optimal Control Problems by Direct Collocation," Optimal Control, edited by R. Bulirsch, A. Miele and J. Stoer, Birkhauser Verlag, Basel, Switzerland, 1993, pp. 129-143.