References

[ocots]

Some useful references.

[ocots]

Feasible trajectories and initial guess

Kiessling, D., Baumgärtner, K., Frey, J., Decré, W., Swevers, J., & Diehl, M. (2024). Fast generation of feasible trajectories in direct optimal control. IEEE Control Systems Letters, 8, 1168-1173.

Note

It would be nice to have an algorithm to get the closest feasible trajectory with a better cost of a reference given trajectory (trajectory in the sense pair of control-state).

Betts, J. T., Campbell, S. L., & Digirolamo, C. (2019). Initial guess sensitivity in computational optimal control problems. Numerical Algebra, Control and Optimization, 10(1), 39-43.

[ocots]

Nonsmooth and sliding modes

Pytlak, R., Suski, D., & Tarnawski, T. (2017). Optimal control of hybrid systems with sliding modes. In Dynamical Systems Theory and Applications (pp. 283-293). Cham: Springer International Publishing.

Nurkanović, A., Sperl, M., Albrecht, S., & Diehl, M. (2024). Finite elements with switch detection for direct optimal control of nonsmooth systems. Numerische Mathematik, 156(3), 1115-1162.

Kazi, S. R., Thombre, M., & Biegler, L. (2024). Globally convergent method for optimal control of hybrid dynamical systems. IFAC-PapersOnLine, 58(14), 868-873.

[ocots]

Optimal Control and GPU

Jeon, S. H., Hong, S., Lee, H. J., Khazoom, C., & Kim, S. (2024). Cusadi: A gpu parallelization framework for symbolic expressions and optimal control. IEEE Robotics and Automation Letters.

Pacaud, F., Nurkanović, A., Pozharskiy, A., Montoison, A., & Shin, S. (2025). An Augmented Lagrangian Method on GPU for Security-Constrained AC Optimal Power Flow. arXiv preprint arXiv:2510.13333.

Gondosiswanto, E., Pulsipher, J.L., 2025. Advances to modeling and solving infinitedimensional optimization problems in InfiniteOpt.jl. Digital Chem. Eng. 15, 100236.

[ocots]

Singular control

Oscillations in direct methods:

Diehl, M., & Gros, S. (2011). Numerical optimal control. Optimization in Engineering Center (OPTEC), 258.

Algorithms:

Foroozandeh, Z., Shamsi, M., & Do Rosário De Pinho, M. (2018). A hybrid direct–indirect approach for solving the singular optimal control problems of finite and infinite order. Iranian Journal of Science and Technology, Transactions A: Science, 42(3), 1545-1554.

Aghaee, M., & Hager, W. W. (2021). The switch point algorithm. SIAM Journal on Control and Optimization, 59(4), 2570-2593.

Hager, W. W. (2023). Extension of switch point algorithm to boundary-value problems. Computational Optimization and Applications, 86(3), 1229-1246.

Andrés‐Martínez, O., Flores‐Tlacuahuac, A., Kameswaran, S., & Biegler, L. T. (2019). An efficient direct/indirect transcription approach for singular optimal control. AIChE Journal, 65(3), 937-946.

Sundaralingam, R. (2023). A two-step method for solving singular control problems. International Journal of Control, 96(9), 2313-2328.

[ocots]

Direct transcription

Kelly, M. P. (2017). Transcription methods for trajectory optimization: a beginners tutorial. arXiv preprint arXiv:1707.00284.

[ocots]

Newton method and indirect shooting

Gerdts, M. (2008). A nonsmooth Newton’s method for control-state constrained optimal control problems. Mathematics and Computers in Simulation, 79(4), 925-936.

Antony, T. (2018). Large scale constrained trajectory optimization using indirect methods (Doctoral dissertation, Purdue University).

[jbcaillau]

thanks @ocots