Jump to content

Unscented optimal control

Add links
From Wikipedia, the free encyclopedia

In mathematics, unscented optimal control combines the notion of the unscented transform with deterministic optimal control to address a class of uncertain optimal control problems.[1][2][3][4] It is a specific application of tychastic optimal control theory,[1][5][6][7] which is a generalization of Riemmann-Stieltjes optimal control theory,[8][9] a concept introduced by Ross and his coworkers.

Mathematical description

[edit]

Suppose that the initial state of a dynamical system,

is an uncertain quantity. Let be the sigma points. Then sigma-copies of the dynamical system are given by,

Applying standard deterministic optimal control principles to this ensemble generates an unscented optimal control.[10][11][12] Unscented optimal control is a special case of tychastic optimal control theory.[1][5][13] According to Aubin[13] and Ross,[1] tychastic processes differ from stochastic processes in that a tychastic process is conditionally deterministic.

Applications

[edit]

Unscented optimal control theory has been applied to UAV guidance,[12][14] spacecraft attitude control,[6] air-traffic control[15] and low-thrust trajectory optimization[2][10]

References

[edit]
  1. ^ a b c d Ross, Isaac (2015). A primer on Pontryagin's principle in optimal control. San Francisco: Collegiate Publishers. pp. 75–82. ISBN 978-0-9843571-1-6.
  2. ^ a b Ross, I. Michael; Proulx, Ronald; Karpenko, Mark (August 4–7, 2014). Unscented Optimal Control for Orbital and Proximity Operations in an Uncertain Environment: A New Zermelo Problem. AIAA/AAS Astrodynamics Specialist Conference. San Diego, CA: American Institute of Aeronautics and Astronautics. doi:10.2514/6.2014-4423. Retrieved August 23, 2024.
  3. ^ Ross et al, Unscented Control for Uncertain Dynamical Systems, US Patent US 9,727,034 Bl. Issued Aug 8, 2017. https://calhoun.nps.edu/bitstream/handle/10945/55812/USPN%209727034.pdf?sequence=1&isAllowed=y
  4. ^ Manchester, Zachary; Kuindersma, Scott (December 2016). "Derivative-free trajectory optimization with unscented dynamic programming". 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE. pp. 3642–3647. doi:10.1109/cdc.2016.7798817. ISBN 978-1-5090-1837-6.
  5. ^ a b Ross, I. Michael; Karpenko, Mark; Proulx, Ronald J. (July 2016). "Path constraints in tychastic and unscented optimal control: Theory, application and experimental results". 2016 American Control Conference (ACC). IEEE. pp. 2918–2923. doi:10.1109/acc.2016.7525362. ISBN 978-1-4673-8682-1. S2CID 1123147.
  6. ^ a b Ross, I. M.; Karpenko, M.; Proulx, R. J. (July 2016). "Path constraints in tychastic and unscented optimal control: Theory, application and experimental results". 2016 American Control Conference (ACC). pp. 2918–2923. doi:10.1109/acc.2016.7525362. ISBN 978-1-4673-8682-1. S2CID 1123147.
  7. ^ Ross, I. M.; Proulx, R. J.; Karpenko, M. (2024-05-04). "Unscented Trajectory Optimization". arXiv:2405.02753 [math.OC].
  8. ^ Ross, I. Michael; Karpenko, Mark; Proulx, Ronald J. (2015). "Riemann-Stieltjes Optimal Control Problems for Uncertain Dynamic Systems". Journal of Guidance, Control, and Dynamics. 38 (7). AIAA: 1251–1263. Bibcode:2015JGCD...38.1251R. doi:10.2514/1.G000505. hdl:10945/48189. S2CID 121424228.
  9. ^ Karpenko, Mark; Proulx, Ronald J. (2016). "Experimental Implementation of Riemann–Stieltjes Optimal Control for Agile Imaging Satellites". Journal of Guidance, Control, and Dynamics. 39 (1): 144–150. Bibcode:2016JGCD...39..144K. doi:10.2514/1.g001325. hdl:10945/50355. ISSN 0731-5090. S2CID 116887441.
  10. ^ a b Ozaki, Naoya; Funase, Ryu (January 8–12, 2018). Tube Stochastic Differential Dynamic Programming for Robust Low-Thrust Trajectory Optimization Problems. 2018 AIAA Guidance, Navigation, and Control Conference. Kissimmee, Florida. doi:10.2514/6.2018-0861.
  11. ^ "Robust Differential Dynamic Programming for Low-Thrust Trajectory Design: Approach with Robust Model Predictive Control Technique" (PDF).
  12. ^ a b Shaffer, R.; Karpenko, M.; Gong, Q. (July 2016). "Unscented guidance for waypoint navigation of a fixed-wing UAV". 2016 American Control Conference (ACC). pp. 473–478. doi:10.1109/acc.2016.7524959. ISBN 978-1-4673-8682-1. S2CID 11741951.
  13. ^ a b Aubin, Jean-Pierre; Saint-Pierre, Patrick (2008). "A Tychastic Approach to Guaranteed Pricing and Management of Portfolios under Transaction Constraints". Seminar on Stochastic Analysis, Random Fields and Applications V. Progress in Probability. Vol. 59. Basel: Birkhäuser Basel. pp. 411–433. doi:10.1007/978-3-7643-8458-6_22. ISBN 978-3-7643-8457-9. Retrieved 2020-12-23.
  14. ^ Ross, I. M.; Proulx, R. J.; Karpenko, M. (July 2015). "Unscented guidance". 2015 American Control Conference (ACC). pp. 5605–5610. doi:10.1109/acc.2015.7172217. ISBN 978-1-4799-8684-2. S2CID 28136418.
  15. ^ Ng, Hok Kwan (2020-06-08). "Strategic Planning with Unscented Optimal Guidance for Urban Air Mobility". AIAA Aviation 2020 Forum. American Institute of Aeronautics and Astronautics. doi:10.2514/6.2020-2904. ISBN 978-1-62410-598-2. S2CID 225658104. Retrieved 2020-12-23.


Stub icon

This mathematics-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Unscented_optimal_control&oldid=1248147517"