Examples Included with GPOPS-II

GPOPS-II includes several examples of varying complexity and all taken from the open literature. Users are welcome to submit new examples to be included in the software, but it is required that any such examples can be used without any restrictions. Currently, the following examples are included with GPOPS-II:


Brachistochrone Problem (citation: General Reference to Calculus of Variations Literature)

Bryson-Denham Problem (citation: Bryson, A. E. and Ho, Y-C, Applied Optimal Control, Hemisphere Publishing, New York, 1975)

Dynamic Soaring Problem (citation: Zhao, Y. J., “Optimal Patterns of Glider Dynamic Soaring,” Optimal Control Applications and Methods, Vol. 24, No. 4, 2004, pp. 67 - 89)

Hyper-Sensitive Problem (citation: Rao, A. V. and Mease, K. D., “Eigenvector Approximate Dichotomic Basic Method for Solving Hyper-Sensitive Optimal Control Problems,” Optimal Control Applications and Methods, Vol. 21, No. 1., 2000, pp. 1-19)

Kinetic Batch Reactor (citation: Betts, J. T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM Press, Philadelphia, 2009)

Launch Vehicle Ascent Problem (citation: 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, April-June 2010, Article 22, 39 pages)

Low-Thrust Orbit Transfer Problem (citation: citation: Betts, J. T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM Press, Philadelphia, 2009)

Minimum Time-to-Climb of a Supersonic Aircraft (citation: Bryson, A. E., Desai, M. and Hofffman, W. C., “Energy-State Approximation in Performance Optimization of Supersonic Aircraft,” Journal of Aircraft, Vol. 6, No. 12, 1969, pp. 418-488)

Moon Lander Problem (citation: Meditch, J., “On the Problem of Optimal Thrust Programming for a Lunar Soft Landing,” IEEE Transactions on Automatic Control, Vol. 9, No. 4, October 1964, pp. 477-484)

Orbit-Raising Problem (citation: Bryson, A. E. and Ho, Y-C, Applied Optimal Control, Hemisphere Publishing, New York, 1975)

Reusable Launch Vehicle Entry Problem (citation: Betts, J. T., Practical Methods for Optimal Control Using Nonlinear Programming, SIAM Press, Philadelphia, 2009)

Robot Arm Problem (citation: Betts, J. T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM Press, Philadelphia, 2009)

Space Station Attitude Control Problem (citation: Betts, J. T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM Press, Philadelphia, 2009)

Tumor Anti-Angiogenesis Problem (citation: Ledzcewicz, U. and Schaettler, H., “Analysis of Optimal Controls for a Mathematical Model in Tumor Anti-Angiogenesis,” Optimal Control Applications and Methods, Vol. 29, No. 1, January-February, 2008, pp. 41-57)









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