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. It is a specific application of tychastic optimal control theory, which is a generalization of Riemmann-Stieltjes optimal control theory, a concept introduced by Ross and his coworkers.

Suppose that the initial state ${\displaystyle x^{0}}$of a dynamical system,

${\displaystyle {\dot {x}}=f(x,u,t)}$

is an uncertain quantity. Let ${\displaystyle \mathrm {X} ^{i}}$be the sigma points. Then sigma-copies of the dynamical system are given by,

${\displaystyle {\dot {\mathrm {X} }}^{i}=f(\mathrm {X} ^{i},u,t)}$

Applying standard deterministic optimal control principles to this ensemble generates an unscented optimal control. 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.

Unscented optimal control theory has been applied to UAV guidance, spacecraft attitude control, air-traffic control and low-thrust trajectory optimization