Examples Included in GPOPS Distribution
Many examples are included in the distribution of GPOPS. These examples range from simple single-phase problems to complex multiple-phase problems. Currently, the following examples (all taken from the open literature) are included with GPOPS:
Brachistochrone Problem (citation: 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,” submitted to Automatica, September 2009.)
Bryson Maximum-Range Problem (citation: Bryson, A. E. and Ho, Y-C, Applied Optimal Control, Hemisphere Publishing, Mineola, New York, 1975)
Bryson-Denham Problem (citation: Bryson, A. E., Denham, W. F., and Dreyfus, S. E., “Optimal Programming with Inequality Constraints I: Necessary Conditions for Extremal Solutions,” AIAA Journal, Vol. 1, No. 11, November 1963, pp. 2544-2550)
Chemical Process Problem (citation: Kokotovic, P., Khalil, H., and O’Reilly, J., Singular Perturbation Methods in Control, Academic Press, SIAM Press, Philadelphia, 1999)
Dynamic Soaring Problem (citation: Zhao, Y. J., “Optimal Patterns of Glider Dynamic Soaring,” Optimal Control Applications and Methods, Vol. 24, No. 2, 2004, pp. 67-89.)
Goddard Rocket Problem (citation: http://www.mcs.anl.gov/~more/cops/bcops/rocket.html)
Hyper-Sensitive Problem (citation: Rao, A. V. and Mease, K. D., “Eigenvector Approximate Dichotomic Basis Method for Solving Hyper-Sensitive Optimal Control Problems,” Optimal Control Applications and Methods, Vol. 21, No. 1, 2000, pp. 1-19.)
Launch Vehicle Ascent Problem (citation: Benson, D. A., A Gauss Pseudospectral Transcription for Optimal Control, PhD Thesis, Department of Aeronautics and Astronautics, MIT, November 2004.)
Linear Tangent Steering Problem (citation: Betts, J. T., Practical Methods for Optimal Control Using Nonlinear Programming, SIAM Press, Philadelphia, 2001)
Minimum Time-to-Climb of a Supersonic Aircraft (Rao, A. V., Extension of a Computational Singular Perturbation Methodology to Optimal Control Problems, Ph.D. Thesis, Department of Mechanical and Aerospace Engineering, Princeton University, June 1996)
Moon-Lander Problem (citation: Meditch, J., “On the Problem of Optimal Thrust Programming for a Soft Lunar Landing,” IEEE Transactions on Automatic Control, Vol. 9, No. 4, 1964, pp. 477-484)
Reusable Launch Vehicle Entry (citation: Betts, J. T., Practical Methods for Optimal Control Using Nonlinear Programming, SIAM Press, Philadelphia, 2001).
If you have examples that you would like to have considered for inclusion in GPOPS, please contact one of the system administrators shown on the inquiries web page. An absolute requirement for any example to be included with GPOPS is that it have no restrictions whatsoever. Any contributed examples will be given their due citation in the GPOPS distribution.