In mathematics, unscented optimal control combines the notion of the
unscented transform
The unscented transform (UT) is a mathematical function used to estimate the result of applying a given nonlinear transformation to a probability distribution that is characterized only in terms of a finite set of statistics. The most common use of ...
with deterministic
optimal control to address a class of uncertain optimal control problems.
[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)
] It is a specific application of
Riemmann-Stieltjes optimal control theory, a concept introduced by
Ross Ross or ROSS may refer to:
People
* Clan Ross, a Highland Scottish clan
* Ross (name), including a list of people with the surname or given name Ross, as well as the meaning
* Earl of Ross, a peerage of Scotland
Places
* RoSS, the Republic of Sout ...
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.
[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)
] Unscented optimal control is a special case of
tychastic optimal control theory.
According to Aubin
and Ross,
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,
spacecraft attitude control, air-traffic control
and low-thrust trajectory optimization
References
Optimal control
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