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.)

__Free Flying Robot__ (citation: Sakawa, Y., “Trajectory Planning of a Free-Flying Robot Using the Optimal Control,” *Optimal Control Applications and Methods*, Vol. 20, No. 5, 1999, pp. 235 - 248.)

__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.)

**Maximum Range of a Hang Glider** (citation: citation: Bulirsch, R., Nertz, E., Pesch, H. J., and von Stryk, O., "Combining Direct and Indirect Methods in Optimal Control: Range Maximization of a Hang Glider," in *Optimal Control*, Bulirsch, R., Miele, A., Stoer, J., Well, K. H., eds. Vol. 111 of International Series of Numerical Mathematics, Birkhauser Verlag, Basel, 1993, pp. 273-288.)

__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)

__Two-Strain Tuberculosis Problem__ (citation: Jung, E., Lenhart, S., and Feng, Z., "Optimal Control of Treatments in a Two-Strain Tuberculosis Model," *Discrete and Continuous Dynamical Systems - Series B*, Vol. 2. No. 4, November 2002, pp. 473-482.)

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