Pseudospectral optimal control for military and industrial applications

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 4128-4142

  Gong, Qi ^a   Kang, Wei ^b   Bedrossian, Nazareth S ^c   Fahroo, Fariba ^d   Sekhavat, Pooya ^b   Bollino, Kevin ^e  

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

^b NAVAL POSTGRADUATE SCHOOL   (United States)

^c CHARLES STARK DRAPER LABORATORY   (United States)

^d Computational Mathematics ^*  (United States)

^e Air Force Element of Space Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INDUSTRIAL APPLICATIONS; MILITARY APPLICATIONS; NUMERICAL METHODS; PROBLEM SOLVING; SYSTEMS ENGINEERING;

ADVANCED TECHNOLOGY; PSEUDOSPECTRAL OPTIMAL CONTROL; THEORETICAL FOUNDATIONS; TUTORIAL SECTION;

OPTIMAL CONTROL SYSTEMS;

EID: 62749122719     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4435052     Document Type: Conference Paper

References (50)

1. J. T. Betts, N. Biehn and S. L. Campbell, Convergence of nonconvergent IRK discretizations of optimal control problems with state inequality constraints, SIAM Journal Scientific Computation 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 Method in Fluid Dynamics, New York: Springer-Verlag, 1988.
4. H. Choset, et al., Principles of robot motion; theory, algorithms, and implementation, The MIT Press, 2005.
5. J. Cullum, Finite-dimensional approximations of state constrainted continuous optimal problems, SIAM J. Control, Vol. 10, pp. 649-670, 1972.
6. A. L. Dontchev, Discrete approximations in optimal control, Non-smooth Analysis and Geometric Methods in Deterministic Optimal Control, IMA Vol. Math. Appl., 78, Springer, New York, 1996, pp. 59-81. MR 97h:49043.
7. A. L. Dontchev and W. W. Hager, The Euler approximation in state constrained optimal control, Mathematics of Computation, Vol. 70, pp. 173-203, 2001.
8. 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.
9. 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.
10. F. Fahroo and I. M. Ross, Radau pseudospectral methods for infinite-horizon nonlinear optimal control problems, Proc. AIAA Guid., Nav. and Control Conf., San Franscro, CA, 2005.
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, Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control, to appear in Computational Optimization and Applications, 2008.
14. 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.
15. Q. Gong and I. M. Ross, Autonomous pseudospectral knotting methods, 16th AAS/AIAA Space Flight Mechanics Conference, AAS 06-151, Tampa, Florida, Jan., 2006.
16. Q. Gong, W. Kang and I. M. Ross, A pseudospectral observer design method for nonlinear systems, Discrete and Continuous Dynamical Systems Series B, Vol 8, No 3, pp. 589-611, 2007.
17. Q. Gong, I. M. Ross and W. Kang, A unified pseudospectral framework for nonlinear controller and observer design, American Control Conference, pp. 1943-1949, New York City, NY, July, 2007.
18. W. W. Hager, Runge-Kutta methods in optimal control and the transformed adjoint system, Numerische Mathematik, Vol. 87, pp. 247-282, 2000.
19. C. R. Hargraves and S. W. Paris, Direct Trajectory Optimization Using Nonlinear Programming and Collocation, Journal of Guidance, Control and Dynamics, Vol.10, pp.338-342, 1987.
20. A. M. Hawkins, T. R. Fill, R. J. Proulx, E. M. Feron, Constrained Trajectory Optimization for Lunar Landing, AAS Spaceflight Mechanics Meeting, Tampa, FL, January 2006, AAS 06-153.
21. S. I. Infeld and W. Murray, Optimization of stationkeeping for a Libration point mission, AAS Spaceflight Mechanics Meeting, Maui, HI, February 2004. AAS 04-150.
22. W. Kang, M. Ross, and Q. Gong, Pseudospectral Optimal Control and Its Convergence Theorems, Lecture Notes in Control and Information Sciences, Alessandro Astolfi and Lorenzo Marconi eds., Springer, to appear.
23. W. Kang, Q. Gong and I. M. Ross, Convergence of pseudospectral methods for nonlinear optimal control problems with discontinuous controller, 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05), pp. 2799-2804, Seville, Spain, 2005.
24. W. Kang, Q. Gong, I. M. Ross and F. Fahroo, On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable control systems, to appear in International Journal on Robust and Nonlinear Control, 2007.
25. W. Kang, On the Existence and Convergence of Solutions for Legendre Pseudospectral Optimal Control, preprint.
26. L. R. Lewis, Rapid motion planning and autonomous obstacle avoidance for Unmanned Vehicles, Master's Thesis, Naval Postgraduate School, December 2006.
27. P. Lu, H. Sun and B. Tsai, Closed-Loop endoatmospheric ascent guidance, Journal of Guidance, Control and Dynamics, Vol. 26, No. 2, pp. 283-294, 2003.
28. 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.
29. S. W. Paris and C. R. Hargraves, OTIS 3.0 Manual, Boeing Space and Defense Group, Seattle, WA, 1996.
30. E. Polak, Optimization: Algorithms and Consistent Approximations, Springer-Verlag, Heidelberg, 1997.
31. J. Rea, Launch vehicle trajectory optimization using a Legendre pseudospectral method, Proceedings of the AIAA Guidance, Navigation and Control Conference, Austin, TX, Paper No. AIAA 2003-5640, August 2003.
32. I. M. Ross, Q. Gong, F. Fahroo and W. Kang, Practical stabilization through real-time optimal control, Proc. of American Control Conference, pp. 304-309, Minneapolis, MN, June, 2006.
33. I. M. Ross, A historical introduction to the covector mapping principle, Advances in the Astronautical Sciences: Astrodynamics 2005, Vol. 122, Paper AAS 05-332, August 2005.
34. I. M. Ross, User's manual for DIDO: A MATLAB application package for solving optimal control problems, Elissar LLC., Technical Report TR-705, 2007.
35. I. M. Ross and F. Fahroo, A unified framework for real-time optimalcontrol, Proceedings of the IEEE Conference on Decision and Control, Maui, December, pp. 2210-2215, 2003.
36. I. M. Ross and C. N. D'Souza, Hybrid Optimal Control Framework for Mission Planning, J. of Guid., Contr. and Dyn., Vol. 28, No. 4, pp. 686-697, 2005.
37. I. M. Ross, P. Sekhavat, A. Fleming and Q. Gong, Pseudospectral feedback control: foundations, examples and experimental results, AIAA Guidance, Navigation, and Control Conference, AIAA-2006-6354, Keystone, Colorado, Aug., 2006,
38. also to appear in AIAA Journal of Guidance, Control and Dynamics, 2007.
39. I. M. Ross and F. Fahroo, Pseudospectral knotting methods for solving optimal control problems, AIAA Journal of Guidance, Control and Dynamics, Vol. 27, No. 3, pp. 397-405, 2004.
40. I. M. Ross and F. Fahroo, A perspective on methods for trajectory optimization, Proceedings of the AIAA/AAS Astrodynamics Conference, Monterey, CA, August 2002. AIAA Paper No. 2002-4727.
41. I. M. Ross and F. Fahroo, A pseudospectral transformation of the covectors of optimal control systems, Proceedings of the First IFAC Symposium on System Structure and Control, Prague, Czech Republic, 29-31 August 2001.
42. 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.
43. P. Sekhavat and I. M. Ross, On Closed-Loop Spacecraft Attitude Maneuvers, AAS Astrodynamics Specialist Conference, Mackinac Island, MI, August 2007, AAS 07-354.
44. P. Sekhavat, A. Fleming and I. M. Ross, Time-Optimal Nonlinear Feedback Control for the NPSAT1 Spacecraft, Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM 2005, 2428 July 2005 Monterey, CA.
45. S. Stanton, R. Proulx and C. N. 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.
46. L. N. Trefethen, Spectral Methods In MATLAB, SIAM, Philadelphia, PA, 2000.
47. General Atomics Aeronautical Systems, "Aircraft Platforms: Altair," [http://www.ga-asi.com/products/index.php], 26 October 2006.
48. V. M. Veliov, On the Time-discretization of Control Systems, SIAM J. Control Optim., Vol. 35, No. 5, pp. 1470-1486, 1997.
49. 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.
50. H. Yan and K. T. Alfriend, Three-axis Magnetic Attitude Control Using Pseudospectral Control Law in Eccentric Orbits, AAS Spaceflight Mechanics Meeting, Tampa, FL, January 2006, AAS 06-103.