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.)

**(citation: Bryson, A. E. and Ho, Y-C,**

__Bryson-Denham Problem__*Applied Optimal Control*, Hemisphere Publishing, New York, 1975.)

**(citation: Zhao, Y. J., “Optimal Patterns of Glider Dynamic Soaring,”**

__Dynamic Soaring Problem__*Optimal Control Applications and Methods*, Vol. 24, No. 4, 2004, pp. 67 - 89.)

**(citation: Sakawa, Y., “Trajectory Planning of a Free-Flying Robot Using the Optimal Control,”**

__Free Flying Robot__*Optimal Control Applications and Methods*, Vol. 20, No. 5, 1999, pp. 235 - 248.)

**(citation: Rao, A. V. and Mease, K. D., “Eigenvector Approximate Dichotomic Basic Method for Solving Hyper-Sensitive Optimal Control Problems,”**

__Hyper-Sensitive Problem__*Optimal Control Applications and Methods*, Vol. 21, No. 1., 2000, pp. 1-19.)

**(citation: Betts, J. T.,**

__Kinetic Batch Reactor__*Practical Methods for Optimal Control and Estimation Using Nonlinear Programming*, SIAM Press, Philadelphia, 2009)

**(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,”**

__Launch Vehicle Ascent Problem__*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.)

**(citation: Bryson, A. E., Desai, M. and Hofffman, W. C., “Energy-State Approximation in Performance Optimization of Supersonic Aircraft,”**

__Minimum Time-to-Climb of a Supersonic Aircraft__*Journal of Aircraft*, Vol. 6, No. 12, 1969, pp. 418-488.)

**(citation: Meditch, J., “On the Problem of Optimal Thrust Programming for a Lunar Soft Landing,”**

__Moon Lander Problem__*IEEE Transactions on Automatic Control*, Vol. 9, No. 4, October 1964, pp. 477-484)

**(citation: Bryson, A. E. and Ho, Y-C,**

__Orbit-Raising Problem__*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)

**(citation: Ledzcewicz, U. and Schaettler, H., “Analysis of Optimal Controls for a Mathematical Model in Tumor Anti-Angiogenesis,”**

__Tumor Anti-Angiogenesis Problem__*Optimal Control Applications and Methods*, Vol. 29, No. 1, January-February, 2008, pp. 41-57)

**(citation: Jung, E., Lenhart, S., and Feng, Z., "Optimal Control of Treatments in a Two-Strain Tuberculosis Model,"**

__Two-Strain Tuberculosis Problem__*Discrete and Continuous Dynamical Systems - Series B*, Vol. 2. No. 4, November 2002, pp. 473-482.)

Image courtesy of NASA.