GPOPS-II - Next-Generation Optimal Control Software

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    • Brachistochrone Problem
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JOURNAL PUBLICATIONS RELATED TO GPOPS-II

1. Hager, W. W., Hou, H., Mohapatra, S., and Rao, A. V., "Convergence Rate for an hp Collocation Method Applied to Unconstrained Optimal Control," Numerische Mathematik, Submitted for Publication, May 2016.
2. Weinstein, M. J. and Rao, A. V., "Algorithm: ADiGator, a Toolbox for the Algorithmic Differentiation of Mathematical Functions in MATLAB Using Source Transformation via Operator Overloading," ACM Transactions on Mathematical Software, In Revision, May 2016.
3. Cannataro, B., Rao, A. V., and Davis, T. A., "State-Defect Pairing Graph Coarsening Method for Karush-Kuhn-Tucker Matrices Arising in Orthogonal Collocation Methods for Optimal Control," Computational Optimization and Applications, Vol. 64, No. 3, July 2016, pp. 793 - 819.
4. Weinstein, M. J. and Rao, A. V., “A Source Transformation via Operator Overloading Method for the Automatic Differentiation of Mathematical Functions in MATLAB,” ACM Transactions on Mathematical Software, Vol. 42, No. 2, Article 11, June 2016, pp. 11:1 - 11:44.
5. De Groote, F., Kinney, A. L., Rao, A. V., and Fregly, B. J. "Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem," Annals of Biomedical Engineering, Accepted for Publication, March 2016.
6. Graham, K. F. and Rao, A. V., "Minimum-Time Trajectory Optimization of Low-Thrust Earth-Orbit Transfers with Eclipsing," Journal of Spacecraft and Rockets, Vol. 53, No. 2, March - April 2016, pp. 289 - 303.
7. Liu, F., Hager, W. W., and Rao, A. V., “Adaptive Mesh Refinement for Optimal Control Using Nonsmoothness Detection and Mesh Size Reduction,” Journal of the Franklin Institute, Vol. 352, No. 10, October 2015, pp. 4081 - 4106. DOI: 10.1016/j.franklin.2015.05.028.
8. Graham, K. F. and Rao, A. V., “Minimum-Time Trajectory Optimization of Many Revolution Low-Thrust Earth-Orbit Transfers”, Journal of Spacecraft and Rockets, Vol. 52, No. 3, May - June 2015, pp. 711 - 727. http://arc.aiaa.org/doi/abs/10.2514/1.A33187.
9. Limebeer, D. J. N. and Rao, A. V., “Faster, Higher, and Greener: Vehicular Optimal Control,” IEEE Control Systems Magazine, Vol. 35, No. 2, April 2015, pp. 36 - 56. DOI 10.1109/MCS.2014.2384951.
10. Limebeer, D. J. N, Perantoni, G., and Rao, A. V., “Optimal Control of Formula One Car Energy Recovery Systems,” International Journal of Control, Accepted for Publication, February 2014.
11. Patterson, M. A. and Rao, A. V., “GPOPS-II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming,” ACM Transactions on Mathematical Software, Vol., 41, No. 1, October 2014, pp. 1:1-1:37.
12. Françolin, C. C., Benson, D. A., Hager, W. W., Rao, A. V., “Costate Estimation in Optimal Control Using Integral Gaussian Quadrature Collocation Methods,” Optimal Control Applications and Methods, Submitted, October 2013.
13. Patterson, M. A., Hager, W. W., and Rao. A. V., “A ph Mesh Refinement Method for Optimal Control”, Optimal Control Applications and Methods, Accepted for Publication, January 2014. DOI: 10.1002/oca2114.
14. Senses, B. and Rao, A. V., “Minimum-Fuel Finite-Thrust Low-Earth Orbit Aeroassisted Orbital Transfer of Small Spacecraft,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 6, November - December 2013, pp. 1802 - 1810. Available Online at http://arc.aiaa.org/doi/pdf/10.2514/1.58977. doi 10.2514/1.58977.
15. Francolin, C. C., Rao, A. V., Martel, G., and Duarte, C., “Optimal Control of an Autonomous Surface Vehicle to Improve Connectivity in an Underwater Vehicle Network,” Journal of Aerospace Computing, Information, and Communications, Vol. 9, No. 1, September 2012, pp. 1 - 13.
16. Patterson, M. A. and Rao, A. V., “Exploiting Sparsity in Direct Collocation Pseudospectral Methods for Solving Optimal Control Problems,” Journal of Spacecraft and Rockets, Vol. 39, No. 2, March-April 2012, pp. 364 - 377.
17. Darby, C. L., Garg, D., and Rao, A. V., “Costate Estimation Using Multiple-Interval Pseudospectral Methods,” Journal of Spacecraft and Rockets, Vol. 48, No. 5, September-October 2011, pp. 856-866.
18. Darby, C. L. and Rao, A. V., “Minimum-Fuel Low-Earth Orbit Aeroassisted Orbital Transfer of Small Spacecraft,” Journal of Spacecraft and Rockets, Vol. 48, No. 4, July-August 2011, pp. 618-628.
19. Darby, C. L., Hager, W. W., and Rao, A. V., “An hp-Adaptive Pseudospectral Method for Solving Optimal Control Problems,” Optimal Control Applications and Methods, Vol. 32, No. 4, July-August 2011, pp. 476-502.
20. Garg, D., Patterson, M. A., Darby, C. L., Francolin, C., Huntington, G. T., Hager, W. W., and Rao, A. V., “Direct Trajectory Optimization and Costate Estimation of Finite-Horizon and Infinite-Horizon Optimal Control Problems Using a Radau Pseudospectral Method,” Computational Optimization and Applications, Vol. 49, No. 2, June 2011, pp. 335-358.
21. Darby, C. L., Hager, W. W., and Rao, A. V., “Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method,” Journal of Spacecraft and Rockets, Vol. 48, No. 3, May-June 2011, pp. 433-445.
22. Garg, D., Hager, W. W., and Rao, A. V., “Pseudospectral Methods for Solving Infinite-Horizon Optimal Control Problems, ” Automatica, Vol. 47, No. 4, April 2011, pp. 829-837.
23. Garg, D., Patterson, M. A., Hager, W. W., Rao, A. V., Benson, D. A., and Huntington, G. T., “A Unified Framework for the Numerical Solution of Optimal Control Problems Using Pseudospectral Methods,” Automatica, Vol. 46, No. 11, November 2010, pp. 1843-1851.
24. Rao, A. V., Benson, D. A., Darby, C. L., Patterson, M. A., Francolin, C., Sanders, I., and Huntington, G. T., “GPOPS: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using the Gauss Pseudospectral Method,” ACM Transactions on Mathematical Software, Vol. 37, No. 2, March-April 2010, Article 22, 39 pages.
25. Baumgartner, K. A. C., Rao, A. V., and Ferrari, S., “Optimal Control of an Underwater Sensor Network for Cooperative Target Tracking,” IEEE Journal of Oceanic Engineering, Vol. 34, No. 4, 2009, pp. 678 - 697.
26. Matsumura, T., Gogu, C., Haftka, R., and Rao, A. V., “Aeroassisted Orbital Transfer Considering Thermal Protection System Mass,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 3., May-June 2009, pp. 927-938.
27. Huntington, G. T. and Rao, A. V., “Optimal Reconfiguration of Tetrahedral Spacecraft Formations Using the Gauss Pseudospectral Method,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 3, May-June 2008, pp. 689-698.
28. Huntington, G. T. and Rao, A. V., “Comparison of Local and Global Collocation Methods for Optimal Control,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 2, March-April 2008, pp. 432-436.
29. Huntington, G. T., Benson, D. A., and Rao, A. V., “Optimal Configuration of Tetrahedral Spacecraft Formations,” The Journal of the Astronautical Sciences, Vol. 55, No. 2, April-June 2007, pp. 141-169.
30. Benson, D. A., Huntington, G. T., Thorvaldsen, T. P., and Rao, A. V., “Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method,” Journal of Guidance, Control, and Dynamics, Vol. 29, No. 6, November-December 2006, pp. 1435-1440.

CONFERENCE PUBLICATIONS

1. Françolin, C. C. and Rao, A. V., “Direct Trajectory Optimization and Costate Estimation of State-Inequality Path Constrained Optimal Control Problems Using a Radau Pseudospectral Method,” 2012 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2012-4528, Minneapolis, Minnesota, August 13 - 16, 2012.
2. Hou, H., Hager, W. W., and Rao, A. V., “Convergence of a Gauss Pseudospectral Method for Optimal Control,” 2012 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2012-4452, Minneapolis, Minnesota, August 13 - 16, 2012.
3. Senses, B. and Rao, A. V., “A Preliminary Analysis of Small Spacecraft Finite-Thrust Aeroassisted Orbital Transfer,” 2012 AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2012-4812, Minneapolis, Minnesota, August 13 - 16, 2012.
4. Mohan, K., Patterson, M. A., and Rao, A. V., “Optimal Trajectory and Control Generation for the Landing of Multiple Aircraft in the Presence of Obstacles,” 2012 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2012-4826, Minneapolis, Minnesota, August 13 - 16, 2012.
5. Darby, C. L. Garg, D., and Rao, A. V., “Costate Estimation Using Multiple-Interval Pseudospectral Methods,” 2011 AIAA Guidance, Navigation, and Control Conference, Portland Oregon, August 8 - 11, 2011.
6. Darby, C. L., Hager, W. W., and Rao, A. V., “A Preliminary Analysis of a Variable-Order Approach to Solving Optimal Control Problems Using Pseudospectral Methods,” 2010 AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2010-8272, Toronto, Ontario, Canada, August 2 - 5, 2010.
7. Françolin, C., Rao, A. V., Duarte, C., and Martel, G., “Optimization of the Motion of a Mobile Gateway to Improve Connectivity in a Network of Autonomous Underwater Vehicles,” AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2010-7572, Toronto, Ontario, Canada, August 2 - 5, 2010.
8. Garg, D., Hager, W, W., and Rao, A. V., “Gauss Pseudospectral Method for Solving Infinite-Horizon Optimal Control Problems,” 2010 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2010-7890, Toronto, Ontario, Canada, August 2 - 5, 2010.
9. Jorris, T. R. and Rao, A. V., “Bang-Bang Trajectory Optimization Using Autonomous Phase Placement and Mesh Refinement Satisfying Waypoint and No-Fly Zone Constraints,” 2010 AAS/AIAA Space Flight Mechanics Meeting, AAS Paper Number 10-115, San Diego, California, February 15 - 17, 2010.
10. Darby, C. L., “Optimal Impulsive LEO to LEO Aeroassisted Orbital Transfer of Small Satellites,” 2010 Space Flight Mechanics Meeting, AAS Paper 10-102, San Diego, California, February 15 - 17, 2010.
11. Rao, A. V., “Survey of Numerical Methods for Optimal Control,” 2009 AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 09-334, Pittsburgh, PA, August 10 - 13, 2009.
12. Garg, D., Patterson, M. A., Hager, W. W., Rao, A. V., Benson, D. A., and Huntington, G. T., “An Overview of Three Pseudospectral Methods for the Numerical Solution of Optimal Control Problems,” 2009 AAS/AIAA Astrodynamics Specialist Conference, Pittsburgh, PA, August 10 - 13, 2009.
13. Garg, D., Patterson, M. A., Darby, C. L., Françolin, C., Huntington, G. T., Hager, W. W., and Rao, A. V., “Direct Trajectory Optimization and Costate Estimation of General Optimal Control Problems Using a Radau Pseudospectral Method,” 2009 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2009-5989, Chicago, IL, August 10 - 13, 2009.
14. Darby, C. L. and Rao, A. V., “A State Approximation-Based Mesh Refinement Algorithm for Solving Optimal Control Problems Using Pseudospectral Methods,” 2009 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2009-5791, Chicago, IL, August 10 - 13, 2009.
15. Darby, C. L. and Rao, A. V., “An Initial Examination of Using Pseudospectral Methods for Time-Scale and Differential Geometric Analysis of Nonlinear Optimal Control Problems,” 2008 AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2008-6449, Honolulu, Hawaii, August 18-21, 2008.
16. Rao, A. V., Scherich, A. W., Cox, S., and Mosher, T., “A Concept for Operationally Responsive Space Mission Planning Using Aeroassisted Orbital Transfer,” 2008 AIAA Responsive Space Conference, AIAA Paper RS6-2008-1001, Los Angeles, California, April 2008 - May 1, 2008.
17. Matsumura, T., Gogu, C., Haftka, R., and Rao, A. V., “Aeroassisted Orbital Transfer Trajectory Optimization Considering Thermal Protection System Mass,” 2008 AIAA Aerospace Sciences Meeting, AIAA Papper 2008-898, Reno, Nevada, January 7 - 10, 2008.
18. Huntington, G. T., Benson, D. A., and Rao, A. V., “A Comparison of Accuracy and Computational Efficiency of Three Pseudospectral Methods,” 2007 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2007-6405, Hilton Head, SC, August 20-23, 2007.
19. Huntington, G. T. and Rao, A. V., “A Comparison of Local and Global Orthogonal Collocation Methods for Solving Optimal Control Problems,” 2007 American Control Conference, July 11 - 13, New York.
20. Huntington, G. T., Benson, D. A., and Rao, A. V., “Post-Optimality Analysis and Evaluation of a Formation Flying Problem via a Gauss Pseudospectral Method,” 2005 AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, California, August 2005.
21. Huntington, G. T. and Rao, A. V., “Optimal Reconfiguration of Tetrahedral Spacecraft Formations via a Gauss Pseudospectral Method,” 2005 AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, California, August 2005.
22. Huntington, G. T. and Rao, A. V., “Optimal Configuration of Tetrahedral Spacecraft Formations via a Gauss Pseudospectral Method,” 2005 AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado, January 2005.
23. Rao, A. V., “Extension of a Pseudospectral Legendre Method to Non-Sequential Multiple-Phase Optimal Control Problems,” 2003 AiAA Guidance, Navigation, and Control Conference, AIAA Paper 2003-5634, Austin, TX, August 11 - 14, 2003.
24. Rao, A. V. and Clarke, K. A., “Performance Optimization of a Manuevering Re-entry Vehicle via a Legendre Pseudospectral Method,” 2002 AIAA Atmospheric Flight Mechanics Conference, AIAA Paper 2002-4885, Monterey, California, August 6 - 9, 2002.