A pseudospectral observer for nonlinear systems

Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference

Volumn 1, Issue , 2005, Pages 298-306

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

^a Naval Postgraduate School ^*  (United States)

^b NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; BIFURCATION (MATHEMATICS); CHAOS THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; KALMAN FILTERING; PARAMETER ESTIMATION;

CHAOTIC NONLINEAR SYSTEMS; CONVERGENCE RATE; MEASUREMENT NOISE; PSEUDOSPECTRAL DISCRETIZATIONS;

NONLINEAR SYSTEMS;

EID: 29744464506     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2005-5845     Document Type: Conference Paper

References (27)

1. J. T. Betts, N. Biehn and S. L. Campbell, Convergence Of Non-convergent 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 Non-linear Programming. SIAM, Philadelphia, PA, 2001.
3. A. E. Bryson and Y. C. Ho, Applied Optimal Control. Hemisphere, New York, 1975.
4. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spetral Method in Fluid Dynamics, New York: Springer-Verlag, 1988.
5. 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.
6. P. E. Gill, W. Murray and M. A. Saunders, SNOPT: an SQP algorithm for large-scale constrainted optimisation, SIAM J. of Opt. Vol. 12, No. 4, pp. 979-1006, 2002.
7. G. Elnagar, M. A. Kazemi and M. Razzaghi, The pseudospectral Legendre method for discretizing optimal control problems, IEEE Trans. Automat. Contr., Vol. 40, pp. 1793-1796, 1995.
8. 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.
9. Q. Gong, I. M. Ross, W. Kang and F. Fahroo, Convergence of Pseudospectral Methods for Constrained Nonlinear Optimal Control Problems, Proc. The IASTED International Conference on Intelligent Systems and Control, Honolulu, HI, pp. 209-214, 2004.
10. Q. Gong, W. Kang and I. M. Ross, A pseudospectral method for the optimal control of constrained feedback linearizable systems, to appear in IEEE Conference on Control Applications, Toronto, Canada, 2005.
11. S. J. Julier and J. K. Uhlmann, Unscented filtering and nonlinear estimation, Proceedings of the IEEE, Vol 92, No. 3, pp. 401-422, 2001.
12. W. Kang. Moving horizon numerical observer of nonlinear systems, in preprint, 2001.
13. W. Kang, Q. Gong and I. M. Ross, A pseudospectral method for a class of nonlinear optimal control problems with discontinuous controller, to appear in 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05). Seville, Spain, 2005.
14. A. J. Krener and A. Isidori, Linearization by output injection and nonlinear observers. Systems and Control Letters, pp. 47-52, 1983.
15. A. J. Krener and W. Kang, Locally convergent nonlinear observers. SIAM J. Control Optim., Vol 42, No. 1, pp. 155-177, 2003.
16. A. J. Krener and M. Xiao, Observers for linearly unobservable nonlinear Systems. Systems and Control Letters, Vol. 46, pp. 281-288, 2002.
17. H. Michalska and D. Q. Mayne, Moving horizon observers and observer-based control, IEEE Trans. Automat. Contr., Vol. 40, No. 6, pp. 995-1000, 1995.
18. 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.
19. E. Polak, A historical survey of computations methods in optimal control, SIAM Review. Vol. 15, pp. 553-548, 1973.
20. E. Polak, Optimization: Algorithms and Consistent Approximations, Springer-Verlag, Heidelberg, 1997.
21. C. V. Rao, J. B. Rawlings and D. Q. Mayne, Constrainted state estimation for nonlinear discrete-time systems: stability and moving horizon approximations, IEEE Trans. Automat. Contr., Vol. 48, No. 2, pp. 216-258, 2003.
22. R. Riaza, Double SIB points in differential-algebraic systems, IEEE Trans. Automat. Contr., Vol. 48, No. 9, pp. 1625-1629, 2003.
23. I. M. Ross and F. Fahroo, Psendospectral methods for optimal motion planning of differentially flat systems, IEEE Transactions on Automatic Control, Vol.49, No.8, pp.1410-1413, August 2004.
24. 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.
25. I. M. Ross and F. Fahroo, Issues in the Real-Time Computation of Optimal Control, Mathematical and Computer Modelling, Vol. 40, Pergamon Publication (to appear).
26. I. M. Ross, F. Fahroo and Q. Gong, "A Spectral Algorithm for Pseudospectral Methods in Optimal Control," Proceedings of the 10th International Conference on Cybernetics and Information Technologies, Systems and Applications: CITSA 2004, July 21-25, 2004, Orlando, FL.
27. Strizzi, J., Ross, I. M., and Fahroo, F., "Towards Real-Time Computation of Optimal Controls for Nonlinear Systems," Proceedings of the AIAA Guidance, Navigation and Control Conference, AIAA-2002-4945, Monterey, CA, 5-8 August 2002.