Hybrid optimal control framework for mission planning

Journal of Guidance, Control, and Dynamics

Volumn 28, Issue 4, 2005, Pages 686-697

  Ross, I Michael ^a,c   D'Souza, Christopher N ^b,d  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

^b CHARLES STARK DRAPER LABORATORY   (United States)

^c Department of Mechanical and Astronautical Engineering   (United States)

^d Aerospace Systems

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE ENGINEERING; FINITE AUTOMATA; FLIGHT DYNAMICS; INTEGER PROGRAMMING; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; PLANNING; PROBLEM SOLVING;

CONTINUOUS-TIME MOTION; DIGRAPH; HYBRID OPTIMAL CONTROL; MISSION PLANNING;

SPACE RESEARCH;

EID: 22944490891     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.8285     Document Type: Article

References (55)

1. Betts, J. T., Practical Methods for Optimal Control Using Nonlinear Programming, Advances in Control and Design Series, Society for Industrial and Applied Mathematics, Philadelphia, 2001.
2. Betts, J. T., "Survey of Numerical Methods for Trajectory Optimization," Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998, pp. 193-207.
3. Ross, I. M., and Fahroo, F., "A Perspective on Methods for Trajectory Optimization," AIAA Paper 2002-4727, Aug. 2002.
4. Pesch, H. J., "A Practical Guide to the Solution of Real-Life Optimal Control Problems," Control and Cybernetics, Vol. 23, No. 1/2, 1994, pp. 7-60.
5. Ross, I. M., and Fahroo, F., "Pseudospectral Knotting Methods for Solving Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 27, No. 3, 2004, pp. 397-405.
6. Warner, M. S., and Hodges, D. H., "Solving Optimal Control Problems Using hp-Version Finite Elements in Time," Journal of Guidance, Control, and Dynamics, Vol. 23, No. 1, 2000, pp. 86-94.
7. Milam, M. B., Mushambi, K., and Murray, R. M., "A New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems," Proceedings of the IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2000.
8. Ross, I. M., and Fahroo, F., "Issues in the Real-Time Computation of Optimal Control," Mathematical and Computer Modelling (to be published).
9. Audet, C., and Dennis, J. E., "Pattern Search Algorithms For Mixed Variable Programming," SIAM Journal of Optimization, Vol. 11, No. 3, 2000, pp. 573, 594.
10. Lucidi, S., Piccialli, V., and Sciandrone, M., "An Algorithm Model For Mixed Variable Programming," D.I.S. Technical Rept, 17-02, Univ. of Rome "La Sapienza," Rome, 2002.
11. Kreyzig, E., Advanced Engineering Mathematics, 7th ed., Wiley, New York, 1993, Chap. 22.
12. Stateflow and Stateflow Coder User's Guide, Math Works, Inc., Natick, MA, 2004.
13. Burkard, R. E., Deǐneko, V. G., Van Dal, R., Van der Veen, J. A. A., and Woeginger, G. J., "Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey" SIAM Review, Vol. 40, No. 3, 1998, pp. 496-546.
14. von Stryk, O., and Glocker, M., "Numerical Mixed-Integer Optimal Control and Motorized Traveling Salesmen Problems," APII Journal Europeen des Systèmes Automatises [European Journal of Control], Vol. 35, No. 4, 2001, pp. 519-533.
15. von Stryk, O., and Glocker, M., "Decomposition of Mixed-Integer Optimal Control Problems Using Branch and Bound and Sparse Direct Collocation," Proceedings of ADPM 2000. The 4th International Conference on Automation of Mixed Processes: Hybrid Dynamic Systems, Shaker, Aachen, Germany, 2000, pp. 99-104.
16. Glocker, M., and von Stryk, O., "Hybrid Optimal Control of Motorized Traveling Salesmen and Beyond," Proceedings of the 15th IFAC World Congress on Automatic Control, IFAC, Barcelona, July 2002.
17. Fowler, W. T., and Gottlieb, R. G., "A Result Applicable to a Particular Class of Branched Optimization Problems," Engineering Optimization, Vol. 2, 1977, pp. 223-337.
18. Sussmann, H. J., "A Maximum Principle for Hybrid Optimal Control Problems," Proceedings of the 38th IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, Dec. 1999.
19. Sussmann, H. J., "A Nonsmooth Hybrid Maximum Principle," Lecture Notes in Control and Information Sciences, Vol. 246, Springer-Verlag, New York, 1999, pp. 325-354.
20. Sussmann, H. J., "Set-Valued Differentials and the Hybrid Maximum Principle," Proceedings of the 39th IEEE Conference on Decision and Control, IEEE Press, Piscataway, NJ, 2000.
21. Ross, I. M., and Fahroo, F., "A Direct Method for Solving Nonsmooth Optimal Control Problems," Proceedings of the 2002 World Congress of the International Federation on Automatic Control, IFAC, Barcelona, July 2002.
22. Ross, I. M., and Fahroo, F., "Discrete Verification of Necessary Conditions for Switched Nonlinear Optimal Control Systems," Proceedings of the American Control Conference, Boston, June 2004.
23. Ross, I. M., and D'Souza, C. N., "Rapid Trajectory Optimization of Multi-Agent Hybrid Systems," AIAA Paper 2004-5422, Aug. 2004.
24. Engell, S., Frehse, G., and Schnieder, E. (eds.), Modelling, Analysis and Design of Hybrid Systems, Lecture Notes in Control and Information Sciences, Vol. 279, Springer-Verlag, Berlin, 2002.
25. Antsaklis, P. J., and Nerode, A., "Guest Editorial Hybrid Control Systems: An Introductory Discussion to the Special Issue," IEEE Transactions on Automatic Control, Vol. 43, No. 4, 1998, pp. 457-460.
26. Lygeros, J., Johansson, K. H., Simic, S. N., Zhang, J., and Sastry, S. S., "Dynamical Properties of Hybrid Automata," IEEE Transactions on Automatic Control, Vol. 48, No. 1, 2003, pp. 2-17.
27. Branicky, M. S., Borkar, V. S., and Mitter, S. K., "A Unified Framework for Hybrid Control: Model and Optimal Control Theory," IEEE Transactions on Automatic Control, Vol. 43, No. 1, 1998, pp. 31-45.
28. Buss, M., Glocker, M., Hardt, M., Stryk, O., Bulirsch, R., and Schmidt, G., "Nonlinear Hybrid Dynamical Systems: Modeling, Optimal Control and Applications," Lecture Notes in Control and Information Sciences, Vol. 279, Springer-Verlag, New York, 2002, pp. 311-335.
29. Buss, M., Hardt, M., and von Stryk, O., "Numerical Solution of Hybrid Optimal Control Problems with Applications in Robotics," Proceedings of the 15th IFAC World Congress on Automatic Control, IFAC, Barcelona, July 2002.
30. Zhang, J., Johansson, K. H., Lygeros, J., and Sastry, S., "Zeno Hybrid Systems," International Journal of Robust and Nonlinear Control, Vol. 11, 2001, pp. 435-451.
31. Kolmogorov, A. N., and Fomin, S. V., Elements of the Theory of Functions and Functional Analysis, Dover, Mineola, NY, 1999.
32. Vinter, R. B., Optimal Control, Birkhäuser, Boston, 2000.
33. Hartl, R. F., Sethi, S. P., and Vickson, R. G., "A Survey of the Maximum Principles for Optimal Control Problems with State Constraints," SIAM Review, Vol. 37, No. 2, 1995, pp. 181-218.
34. Stevens, R., and Ross, I. M., "Preliminary Design of Earth-Mars Cyclers Using Solar Sails," Journal of Spacecraft and Rockets, Vol. 42, No. 1, 2005, pp. 132-137; also American Astronautical Society, Paper AAS 03-244, Feb. 2003.
35. Stevens, R., Ross, I. M., and Matousek, S. E., "Earth-Mars Return Trajectories Using Solar Sails," 55th International Astronautical Congress, Vancouver, Paper IAC-04-A.2.08, Oct. 2004.
36. Xu, X., and Antsaklis, P. J., "Results and Perspectives on Computational Methods for Optimal Control of Switched Systems," Proceedings of the Sixth International Workshop on Hybrid Systems: Computation and Control (HSCC 2003), Prague, April 2003.
37. Bardi, M., and Capuzzo-Dolcetta, I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston, 1997.
38. Ross, I. M., and Fahroo, F., "User's Manual for DIDO 2002: A MATLAB Application Package for Dynamic Optimization," NFS Technical Rept. AA-02-002, Dept. of Aeronautics and Astronautics, Naval Postgraduate School, Monterey, CA, June 2002.
39. Elnagar, J., Kazemi, M. A., and Razzaghi, M., "The Pseudospectral Legendre Method for Discretizing Optimal Control Problems," IEEE Transactions on Automatic Control, Vol. 40, No. 10, 1995, pp. 1793-1796.
40. Ross, I. M., and Fahroo, F., "Legendre Pseudospectral Approximations of Optimal Control Problems," Lecture Notes in Control and Information Sciences, Vol. 295, Springer-Verlag, New York, 2003, pp. 327-342.
41. Canute, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988.
42. Gong, Q., Ross, I. M., Kang, W., and Fahroo, F., "Convergence of Pseudospectral Methods for Constrained Nonlinear Optimal Control Problems, " Intelligent Systems and Control, Series on Modelling, Identification and Control, Acta, Calgary, AB, Canada, 2004.
43. Lu, P., Sun, S., and Tsai, B., "Closed-Loop Endoatmospheric Ascent Guidance," Journal of Guidance, Control, and Dynamics, Vol. 26, No. 2, 2003, pp. 283-294.
44. Ross, I. M., and D'Souza, C. N., "Discrete Modeling and Flight Plan Automata for Multi-Agent Launch Systems," NPS Technical Rept., NPS-MAE-04-006, Dept. of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, CA, Sept. 2004.
45. Ross, I. M., King, J. T., and Fahroo, F., "Designing Optimal Spacecraft Formations," AIAA Paper 2002-4635, Aug. 2002.
46. Infeld, S., Josselyn, S., Murray, W., and Ross, I. M., "Design and Control of Libration Point Spacecraft Formations," AIAA Paper 2004-4786, 2004.
47. Weigel, N., and Well, K. H., "Dual Payload Ascent Trajectory Optimization with a Splash-Down Constraint," Journal of Guidance, Control, and Dynamics, Vol. 23, No. 1, 2000, pp. 45-52.
48. Ross, I. M., D'Souza, C. N., Fahroo, F., and Ross, J. B., "A Fast Approach to Multi-Stage Launch Vehicle Trajectory Optimization," AIAA Paper 2003-5639, Aug. 2003.
49. Rea, J., "Launch Vehicle Trajectory Optimization Using a Legendre Pseudospectral Method," AIAA Paper 2003-5640, Aug. 2003.
50. Prussing, J. E., and Conway, B. A., Orbital Mechanics, Oxford Univ. Press, New York, 1993.
51. Ross, I. M., "How to Find Minimum-Fuel Controllers," AIAA Paper 2004-5346, Aug. 2004.
52. Holmström, K., Göran, A. O., and Edvall, M. M., "User's Guide for Tomlab 4.0.6," Tomlab Optimization, Vasteras, Sweden, Aug. 2003.
53. Josselyn, S., and Ross, I. M., "Rapid Verification Method for the Trajectory Optimization of Reentry Vehicles," Journal of Guidance, Control, and Dynamics, Vol. 26, No. 3, 2003, pp. 505-508.
54. Strizzi, J., Ross, I. M., and Fahroo, F., "Towards Real-Time Computation of Optimal Controls for Nonlinear Systems," AIAA Paper 2002-4945, Aug. 2002.
55. Ross, I. M., Fahroo, F., and Gong, Q., "A Spectral Algorithm for Pseudospectral Methods in Optimal Control," Proceedings of the 10th International Conference on Cybernetics and Information Technologies, Systems and Applications (CITSA), CITSA, Orlando, FL, 2004, pp. 104-109.