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.
Mathematical description Suppose that the initial state x 0 {\displaystyle x^{0}} of a dynamical system,
x ˙ = f ( x , u , t ) {\displaystyle {\dot {x}}=f(x,u,t)}
is an uncertain quantity. Let X i {\displaystyle \mathrm {X} ^{i}} be the sigma points. Then sigma-copies of the dynamical system are given by,
X ˙ i = f ( X i , u , t ) {\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.
Applications Unscented optimal control theory has been applied to UAV guidance, spacecraft attitude control, air-traffic control and low-thrust trajectory optimization
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