A unified pseudospectral framework for nonlinear controller and observer design

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 1943-1949

  Gong, Qi ^a   Ross, I Michael ^b   Kang, Wei ^c  

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

^b Naval Postgraduate School ^*  (United States)

^c NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

(I ,J) CONDITIONS; APPLIED (CO); COMPUTATIONAL FRAMEWORK; CONVERGENCE (MATHEMATICS); NON-LINEAR CONTROLLERS; NUMERICAL EXAMPLES; OBSERVER DESIGN; PSEUDOSPECTRAL; PSEUDOSPECTRAL (PS) METHOD; TIME DYNAMIC; UNIFIED FRAMEWORK;

COMPUTATIONAL EFFICIENCY; COMPUTATIONAL METHODS; NONLINEAR SYSTEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 46449137632     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282898     Document Type: Conference Paper

References (34)

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. Comput. 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, Spetral Method in Fluid Dynamics. New York: Springer-Verlag, 1988.
4. A. L. Dontchev, W. W. Hager, and V M. Veliov, Second-order Runge-Kutta approximations in control constrained optimal control, SIAM J. Numerical Analysis, Vol. 38, No.1, pp. 202-226, 2000.
5. F. Fahroo and I. M. Ross, Direct Trajectory Optimization by a Chebyshev Pseudospectral Method, Journal of Guidance, Control and Dynamics, Vol. 25, No. 1, 2002, pp. 160-166.
6. F. Fahroo and I. M. Ross, Costate estimation by a Legendre pseudospectral method, AIAA Journal of Guidance, Control and Dynamics, Vol. 24, No. 2, pp. 270-277, 2001.
7. F. Fahroo and I. M. Ross, Costate estimation by a Legendre pseudospectral method, AIAA Guidance, Navigation and Control Conference, 10-12 August 1998, Boston, MA.
8. F. Fahroo and I. M. Ross, Computational optimal control by spectral collocation with differential inclusion, Proc. of the 1999 Goddard Flight Mechanics Symposium, NASA/CP-1999-209235, pp. 185-200
9. F. Fahroo and I. M. Ross, Radau pseudospectral methods for infinitehorizon nonlinear optimal control problems, Proc. AIAA Guid., Nav. and Control Conf., San Franscro, CA, 2005.
10. J.P. Gauthier, H. Hammouri, and S. Othman, A simple observer for nonlinear systems with applications to bioreactors, IEEE Trans. Automat. Contr., Vol. 37, pp. 875-880, 1992.
11. P. E. Gill, W. Murray and M. A. Saunders, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM J. of Opt., Vol. 12, No. 4, pp. 979-1006, 2002.
12. 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.
13. Q. Gong, I. M. Ross, W. Kang and F. Fahroo, On the pseudospectral covector mapping theorem for nonlinear optimal control, 45th IEEE Conf. on Decision and Control, pp. 2679-2686, San Diago, Dec. 2006.
14. Q. Gong, W. Kang and I. M. Ross, A pseudospectral observer design method for nonlinear systems, AIAA GNC Conference, AIAA-2005-5845, San Francisco, CA, Aug., 2005.
15. 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.
16. 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.
17. W. Kang, Moving horizon numerical observer of nonlinear systems, IEEE Trans. Auto. Cont., Vol. 51, No. 2, Feb. 2006, pp. 344-350.
18. W. Kang, Q. Gong and I. M. Ross, Convergence of pseudospectral methods for a class of discontinuous optimal control, 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05), Seville, Spain, pp. 2799-2804, 2005.
19. P. Lu, H. Sun and B. Tsai, Closed-Loop endoatmospheric ascent guidance, J. Guid., Cont. & Dyn., Vol. 26, No. 2, pp. 283-294, 2003.
20. H. Michalska and D. Q. Mayne, Moving horizon observers and observer-based control, IEEE Trans. Automat. Contr., Vol. 40, No. 6, pp. 995-1006, 1995.
21. P. E. Moraal and J. W. Grizzle, Observer design for nonlinear systems with discrete-time measurements, IEEE Trans. Automat. Contr., Vol. 40, No. 3, pp. 395-404, 1995.
22. S. W. Paris and C. R. Hargraves, OTIS 3.0 Manual, Boeing Space and Defense Group, Seattle, WA, 1996.
23. J. Pietz and N. Bedrossian, Moemtum dumping using only CMGs, Proc. AIAA GNC Conf, Austin, TX, 2003.
24. E. Polak, Optimization: Algorithms and Consistent Approximations, Springer-Verlag, Heidelberg, 1997.
25. C. Qian and W. Lin, A continuous feedback approach to global strong stabilization of nonlinear systems, IEEE Trans. Automat. Contr., Vol. 46, No. 7, pp. 1061-1079, 2001.
26. I. M. Ross and F. Fahroo, Pseudospectral methods for optimal motion planning of differentially flat systems, IEEE Transactions on Automatic Control, Vol.49, No.8, pp.1410-1413, August 2004.
27. I. M. Ross and F. Fahroo, Legendre pseudospectral approximations of optimal control problems, Lecture Notes in Control and Information Sciences, Vol.295, Springer-Verlag, pp. 327-342, New York, 2003.
28. I. M. Ross, Q. Gong, F. Fahroo and W. Kang, Practical stabilization through real-time optimal control, Proc. of American Control Conference, June, 2006.
29. I. M. Ross, P. Sekhavat, Q. Gong and A. Flemming, Pseudospectral Feedback Control: Foundations, Examples and Experimental Results, Proc. AIAA Guidance, Navigation, and Control Conference, Keystone, Colorado, Aug., 2006.
30. I. M. Ross and F. Fahroo, A unified framework for real-time optimal control, Proceedings of the IEEE Conference on Decision and Control, Maui, December, pp. 2210-2215, 2003.
31. 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.
32. S. Stanton, R. Proulx and C. D'Souza, Optimal orbit transfer using a Legendre pseudospectral method, AAS/AIAA Astrodynamics Specialist Conference, AAS-03-574, Big Sky, MT, August 3-7, 2003.
33. L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, PA, 2000.
34. P. Williams, C. Blanksby and P. Trivailo, Receding Horizon Control of Tether System Using Quasilinearization and Chebyshev Pseudospectral Approximations, AAS/AIAA Astrodynamics Specialist Conference, Big Sky, MT, August 3-7, 2003, Paper AAS 03-535.