# List of Nonlinear Dynamic Optimization (NLDO) Examples

| Name | Link | Reference | Solution Type |
| ---- | ---- | ---- | ---- |
| Alp Rider | [alp-rider](alp-rider/) | Bett10 |  |
| Batch Fermentor Penicillin | [batch-fermentor-penicillin](batch-fermentor-penicillin/) | Ban05 |  |
| Brachistochrone | [brachistochrone](brachistochrone/) | Bry75 | closed-form |
| Bryson Ho 59 | [bryson-ho-59](bryson-ho-59/) | Bry75 | closed-form |
| Bryson Ho 63 | [bryson-ho-63](bryson-ho-63/) | Bry75 | partial closed-form |
| Bryson Ho 64 | [bryson-ho-64](bryson-ho-64/) | Bry75 | closed-form |
| Chemical Reactor | [chemical-reactor](chemical-reactor/) | Cit69 |  |
| Container Crane | [container-crane](container-crane/) | Aug01 |  |
| DynamicSoaring | [dynamic-soaring](dynamic-soaring/) | Zhao04 |  |
| Earth Launch | [earth-launch](earth-launch/) | Lon14 |  |
| Free Flying Robot | [free-flying-robot](free-flying-robot/) | Bett10 |  |
| HagerHouRao1 | [hager-hou-rao-1](hager-hou-rao-1/) | Hag16 | closed-form |
| Hang Glider | [hang-glider](hang-glider/) | Bul93 |  |
| HIV Immunology | [hiv-immunology](hiv-immunology/) | Jo02 |  |
| Hypersensitive | [hypersensitive](hypersensitive/) | Rao00 |  |
| Mine Extraction | [mine-extraction](mine-extraction/) |  | closed-form |
| Mountain Car | [mountain-car](mountain-car/) | Mel14 |  |
| Multiextremal | [multiextremal](multiextremal/) | Yu12 |  |
| Neuenhofen Kerrigan X1 | [neuenhofen-kerrigan-x1](neuenhofen-kerrigan-x1/) | Neu20 | partial closed-form |
| Neuenhofen Kerrigan X2 | [neuenhofen-kerrigan-x2](neuenhofen-kerrigan-x2/) | Neu20 | partial closed-form |
| Nonlinear 1D | [nonlinear-1d](nonlinear-1d/) | Garg09 | closed-form |
| Optimal Consumption | [optimal-consumption](optimal-consumption/) | Evans |  |
| Optimal Production and Maintenance | [optimal-production-maintenance](optimal-production-maintenance/) | Cho93 |  |
| Second Order Singular | [second-order-singular](second-order-singular/) | Aly78 | closed-form |
| Semiconductor Laser | [semiconductor-laser](semiconductor-laser/) | Kim04 |  |
| Simple Co-design Transfer | [simple-co-design-transfer](simple-co-design-transfer/) | Her19 |  |
| Simple SASA | [simple-sasa](simple-sasa/) | Her17 | closed-form |
| Simple Suspension | [simple-suspension](simple-suspension/) | Her20 |  |
| Space Shuttle Reentry | [space-shuttle-reentry](space-shuttle-reentry/) | Bett10 |  |
| TimeEnergyInterceptor | [time-energy-interceptor](time-energy-interceptor/) | Ban20 |  |
| Train | [train](train/) | Van01 |  |
| Transfer - Maximum Radius | [transfer-max-radius](transfer-max-radius/) | Bry75 |  |
| Transfer - Minimum Fuel | [transfer-min-fuel](transfer-min-fuel/) | Ross07 |  |
| Transfer - Minimum Time | [transfer-min-time](transfer-min-time/) | Bry75 |  |
| Tuberculosis | [tuberculosis](tuberculosis/) | Bett10 |  |
| Tumor | [tumor](tumor/) | Led08 |  |
| Two Link Robot | [two-link-robot](two-link-robot/) | Lu00 |  |
| van der Pol | [vanderpol](vanderpol/) | Can02 |  |

### References
- [**Aly78**] G. M. Aly, "*The computation of optimal singular control*", International Journal of Control, vol. 28, no. 5, pp. 681–688, Nov. 1978, doi: 10.1080/00207177808922489. [Online]. Available: http://dx.doi.org/10.1080/00207177808922489
- [**Aug01**] D. Augustin and H. Maurer, "*Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints*," in Online Optimization of Large Scale Systems, Springer Berlin Heidelberg, 2001, pp. 69–82
- [**Ban05**] J. R. Banga, E. Balsa-Canto, C. G. Moles, and A. A. Alonso, "*Dynamic optimization of bioprocesses: Efficient and robust numerical strategies*", Journal of Biotechnology, vol. 117, no. 4, pp. 407–419, Jun. 2005, doi: 10.1016/j.jbiotec.2005.02.013. [Online]. Available: http://dx.doi.org/10.1016/j.jbiotec.2005.02.013
- [**Ban20**] A. Banerjee, M. Nabi, and T. Raghunathan, "*Time-energy optimal guidance strategy for realistic interceptor using pseudospectral method*", Transactions of the Institute of Measurement and Control, vol. 42, no. 13. SAGE Publications, pp. 2361–2371, Apr. 21, 2020 [Online]. Available: http://dx.doi.org/10.1177/0142331220910919 
- [**Bett10**] J. T. Betts, "*Practical Methods for Optimal Control and Estimation Using Nonlinear Programming*." Society for Industrial and Applied Mathematics, Jan. 2010, doi: 10.1137/1.9780898718577
- [**Bry75**] A. E. Bryson Jr. and Y.-C. Ho, "*Applied Optimal Control*."" Taylor & Francis, 1975, isbn: 9780891162285
- [**Bul93**] R. Bulirsch, E. Nerz, H. J. Pesch, and O. von Stryk, "*Combining Direct and Indirect Methods in Optimal Control: Range Maximization of a Hang Glider,*" in Optimal Control, Birkhäuser Basel, 1993, pp. 273–288 [Online]. Available: http://dx.doi.org/10.1007/978-3-0348-7539-4_20
- [**Can02**] E. Balsa Canto, J. R. Banga, A. A. Alonso, and V. S. Vassiliadis, "*Restricted second order information for the solution of optimal control problems using control vector parameterization*," Journal of Process Control, vol. 12, no. 2, pp. 243–255, Feb. 2002, doi: 10.1016/s0959-1524(01)00008-7
- [**Cit69**] S. J. Citron, "*Elements of Optimal Control*.", Holt, Rinehart and Winston, 1969
- [**Cho93**] D. I. Cho, P. L. Abad, and M. Parlar, "*Optimal production and maintenance decisions when a system experience age-dependent deterioration*", Optim. Control Appl. Meth., vol. 14, no. 3, pp. 153–167, Jul. 1993, doi: 10.1002/oca.4660140302. [Online]. Available: http://dx.doi.org/10.1002/oca.4660140302
- [**Evans**] L. C. Evans, "*An Introduction to Mathematical Optimal Control Theory*." Department of Mathematics, University of California, Berkeley, Version 0.2
- [**Hag16**] W. W. Hager, H. Hou, and A. V. Rao, "*Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control*", J Optim Theory Appl, vol. 169, no. 3, pp. 801–824, Mar. 2016, doi: 10.1007/s10957-016-0929-7
- [**Her17**] D. R. Herber and J. T. Allison, "*Unified Scaling of Dynamic Optimization Design Formulations*", in Volume 2A: 43rd Design Automation Conference, 2017, doi: 10.1115/detc2017-67676 [Online]. Available: http://dx.doi.org/10.1115/DETC2017-67676
- [**Her19**] D. R. Herber and J. T. Allison, "*Nested and Simultaneous Solution Strategies for General Combined Plant and Control Design Problems*," Journal of Mechanical Design, vol. 141, no. 1, Oct. 2018, doi: 10.1115/1.4040705
- [**Her20**] D. R. Herber and A. K. Sundarrajan, "*On the uses of linear-quadratic methods in solving nonlinear dynamic optimization problems with direct transcription*", in ASME International Mechanical Engineering Congress & Exposition, 2020
- [**Garg09**] D. Garg et al., "*"Direct Trajectory Optimization and Costate Estimation of General Optimal Control Problems Using a Radau Pseudospectral Method*", in AIAA Guidance, Navigation, and Control Conference, 2009, doi: 10.2514/6.2009-5989
- [**Jo02**] H. R. Joshi, "*Optimal control of an HIV immunology model*," Optimal Control Applications and Methods, vol. 23, no. 4, pp. 199–213, 2002, doi: 10.1002/oca.710
- [**Kim04**] J.-H. R. Kim, G. L. Lippi, and H. Maurer, "*Minimizing the transition time in lasers by optimal control methods*", Physica D: Nonlinear Phenomena, vol. 191, no. 3–4, pp. 238–260, May 2004, doi: 10.1016/j.physd.2003.12.002. [Online]. Available: http://dx.doi.org/10.1016/j.physd.2003.12.002
- [**Led08**] U. Ledzewicz and H. Schättler, "*Analysis of optimal controls for a mathematical model of tumour anti-angiogenesis*,"" Optimal Control Applications and Methods, vol. 29, no. 1, pp. 41–57, Jan. 2008, doi: 10.1002/oca.814
- [**Lon14**] J. M. Longuski, J. J. Guzmán, and J. E. Prussing, *Optimal Control with Aerospace Applications*. Springer New York, 2014 [Online]. Available: http://dx.doi.org/10.1007/978-1-4614-8945-0
- [**Lu00**] R. Luus, *Iterative Dynamic Programming*. CRC Press, 2000, isbn: 1584881488
- [**Mel14**] A. A. Melnikov, A. Makmal, H. J. Briegel, "*Projective Simulation Applied to the Grid-World and the Mountain-Car Problem*", ArXiv:1405.5459 [Cs], May 2014. arXiv.org, http://arxiv.org/abs/1405.5459
- [**Neu20**] M. P. Neuenhofen and E. C. Kerrigan, "*An integral penalty-barrier direct transcription method for optimal control*," 2020, arXiv:2009.06217
- [**Rao00**] A. V. Rao and K. D. Mease, "*Eigenvector approximate dichotomic basis method for solving hyper-sensitive optimal control problems*, Optimal Control Applications and Methods, vol. 21, no. 1, pp. 1–19, Jan. 2000, doi: 10.1002/(SICI)1099-1514(200001/02)21:1<1::AID-OCA646>3.0.CO;2-V
- [**Ross07**] I. M. Ross, Q. Gong, and P. Sekhavat, "*Low-Thrust, High-Accuracy Trajectory Optimization*," Journal of Guidance, Control, and Dynamics, vol. 30, no. 4, pp. 921–933, Jul. 2007, doi: 10.2514/1.23181
- [**Van01**] R. J. Vanderbei, "*Case Studies in Trajectory Optimization: Trains, Planes, and Other Pastimes*," Optimization and Engineering, vol. 2, no. 2, pp. 215-243, 2001, doi: 10.1023/a:1013145328012
- [**Yu12**] A. Yu. Gornov, T. S. Zarodnyuk, T. I. Madzhara, A. V. Daneeva, and I. A. Veyalko, "*A Collection of Test Multiextremal Optimal Control Problems*", in Optimization, Simulation, and Control, Springer New York, 2012, pp. 257–274 [Online]. Available: http://dx.doi.org/10.1007/978-1-4614-5131-0_16
- [**Zhao04**] Y. J. Zhao, "*Optimal Pattern of Glider Dynamic Soaring*," Optimal Control Applications and Methods, vol. 25, no. 2, pp. 67-89, 2004, doi: 10.1002/oca.710