On the pseudospectral covector mapping theorem for nonlinear optimal control

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 2679-2686

  Gong, Qi ^a   Ross, I Michael ^b   Kang, Wei ^b   Fahroo, Fariba ^b  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

^b NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

CONSTRAINT QUALIFICATIONS; COVECTOR MAPPING; DISCRETIZED OPTIMAL CONTROL PROBLEMS;

NONLINEAR CONTROL SYSTEMS;

EID: 33845750973     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377729     Document Type: Conference Paper

References (30)

1. J. T. Betts, N. Biehn and S. L. Campbell, Convergence of nonconvergent IRK discretizations of optimal control problems with state inequality constraints, SIAM J. Sci. Comp., Vol. 23, No. 6, pp. 1981-2007, 2002.
2. J. T. Betts, Practical Methods for Optimal Control Using Nonlinear Programming, SIAM, Philadelphia, PA, 2001.
3. C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods in Fluid Dynamics, New York: Springer-Verlag, 1988.
4. A. L. Dontchev and W. W. Hager, The Euler approximation in state constrained optimal control, Math. Comp., Vol. 70, pp. 173-203, 2000.
5. G. Elnagar, M. A. Kazemi and M. Razzaghi, The pseudospectral Legendre method for discretizing optimal control problems, IEEE Trans. Auto. Cont. Vol. 40, pp. 1793-1796, 1995.
6. F. Fahroo and I. M. Ross, Costate estimation by a Legendre pseudospectral method, J. of Guid., Cont. & Dyn., Vol. 24, No. 2, pp. 270-277, 2001.
7. F. Fahroo and I. M. Ross, On discrete-time optimality conditions for pseudospectral methods, Proc. AIAA/AAS Astro. Conf, Keystone, CO, August 2006. AIAA-2006-6304.
8. G. Freud, Orthogonal polynomials, Pergamon Press, 1971.
9. P. E. Gill, W. Murray and M. A. Saunders, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM Review, Vol. 47, No. 1, 2005, pp. 99-131.
10. Q. Gong, W. Kang and I. M. Ross, A pseudospectral method for the optimal control of constrained feedback linearizable systems, IEEE Trans. Auto. Cont., Vol. 51, No. 7, July 2006, pp. 1115-1129.
11. W. W. Hager, Runge-Kutta methods in optimal control and the transformed adjoint system, Numerische Mathematik, Vol. 87, pp. 247-282, 2000.
12. R. F. Hartl, S. P. Sethi and R. G. Vickson, A survey of the maximum principles for optimal control problems with state constraints, SIAM Rev., Vol. 37, No. 2, pp. 181-218, 1995.
13. A. M. Hawkins, T. R. Fill, R. J. Proulx, E. M. Feron, Constrained Trajectory Optimization for Lunar Landing, AAS Spaceflight Mech. Mtg., Tampa, FL, January 2006, AAS 06-153.
14. S. I. Infeld and W. Murray, Optimization of stationkeeping for a Libration point mission, Proc. AAS Spaceflight Mech. Mtg., Maui, HI, February 2004. AAS 04-150.
15. P. Lu, H. Sun and B. Tsai, Closed-Loop endoatmospheric ascent guidance, J. Guid., Cont. & Dyn., Vol. 26, No. 2, pp. 283-294, 2003.
16. B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, vol. 330 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] Series, Springer, Berlin, 2005.
17. J. Nocedal and S. J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.
18. S. W. Paris and C. R. Hargraves, OTIS 3.0 Manual, Boeing Space and Defense Group, Seattle, WA, 1996.
19. J. Pietz and N. Bedrossian, Moemtum dumping using only CMGs, Proc. AIAA GNC Conf., Austin, TX, 2003.
20. E. Polak, Optimization: Algorithms and Consistent Approximations, Springer-Verlag, Heidelberg, 1997.
21. J. Rea, Launch vehicle trajectory optimization using a Legendre pseudospectral method, Proc. AIAA GNC Conf., Austin, TX, Paper No. AIAA 2003-5640, August 2003.
22. I. M. Ross, User's manual for DIDO: A MATLAB application package for solving optimal control problems, Technical Report 04-01.0, Tomlab Optimization Inc, February 2004.
23. I. M. Ross and F. Fahroo, Pseudospectral methods for optimal motion planning of differentially flat systems, IEEE Trans. Auto. Cont., Vol. 49, No. 8, pp. 1410-1413, August 2004.
24. I. M. Ross and F. Fahroo, Legendre pseudospectral approximations of optimal control problems, Lee. Notes in Cont. & Info. Sc., Eds. W. Kang et al, Vol. 295, Springer-Verlag, pp. 327-342, New York, 2003.
25. I. M. Ross and F. Fahroo, A unified framework for real-time optimal control, Proc. IEEE CDC, Maui, December, pp. 2210-2215, 2003.
26. I. M. Ross, P. Sekhavat, A. Fleming and Q. Gong, Pseudospectral feedback control: Foundations, examples and experimental results, Proc. AIAA GNC Conf., 21-24 August 2006, Keystone, CO.
27. S. Stanton, R. Proulx and C. D'Souza, Optimal orbit transfer using a Legendre pseudospectral method, AAS/AIAA Astro. Specialist Conf., AAS-03-574, Big Sky, MT, August 3-7, 2003.
28. L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, PA, 2000.
29. P. Williams, Application of Pseudospectral Methods for Receding Horizon Control, J. Guid., Cont. & Dyn., Vol.27, No.2., 2004, pp. 310-314.
30. H. Yan and K. T. Alfriend, Three-axis Magnetic Attitude Control Using Pseudospectral Control Law in Eccentric Orbits, AAS Spaceflight Mech. Mtg., Tampa, FL, January 2006, AAS 06-103.