JOURNAL PUBLICATIONS RELATED TO GPOPS-II

- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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

- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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.