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 Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and ...

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 Sou ...

and his coworkers.

Mathematical description

Suppose that the initial state

x^0

of a dynamical system,

\dot = f(x, u, t)

is an uncertain quantity. Let

\Chi^i

be the sigma points. Then sigma-copies of the dynamical system are given by,

\dot\Chi^i = f(\Chi^i, u, t)

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 process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...

es 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 {{math-stub