Unscented optimal control
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] It is a specific application of Riemmann-Stieltjes optimal control theory,[4][5] a concept introduced by Ross and his coworkers.
Mathematical description
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.[6][7][8] Unscented optimal control is a special case of tychastic optimal control theory.[1][9][10] According to Aubin[10] and Ross,[1] tychastic processes differ from stochastic processes in that a tychastic process is conditionally deterministic.
Applications
Unscented optimal control theory has been applied to UAV guidance,[8][11] spacecraft attitude control,[12] air-traffic control[13] and low-thrust trajectory optimization[2][6]
References
- ^ ISBN 978-0-9843571-1-6.
- ^ a b Unscented Optimal Control for Orbital and Proximity Operations in an Uncertain Environment: A New Zermelo Problem I. Michael Ross, Ronald Proulx, Mark Karpenko August 2014, American Institute of Aeronautics and Astronautics (AIAA)
- ^ 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
- S2CID 121424228.
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- ^ a b Naoya Ozaki and Ryu Funase. "Tube Stochastic Differential Dynamic Programming for Robust Low-Thrust Trajectory Optimization Problems", 2018 AIAA Guidance, Navigation, and Control Conference, AIAA SciTech Forum, (AIAA 2018-0861)
- ^ "Robust Differential Dynamic Programming for Low-Thrust Trajectory Design: Approach with Robust Model Predictive Control Technique" (PDF).
- ^ S2CID 11741951.
- S2CID 1123147.
- ^ ISBN 978-3-7643-8457-9, retrieved 2020-12-23
- S2CID 28136418.
- S2CID 1123147.
- S2CID 225658104, retrieved 2020-12-23