Abstract
A class of bilinear stochastic control problems involving single-degree-of-freedom rotation is formulated and resolved. Both synchronization control and orientation control are considered. In each case, the measurement data is first processed through a nonlinear transformation. The transformed process then goes through an ordinary estimator, such as a Kalman–Busy filter. After another nonlinear processing of the output of the ordinary estimator, the desired optimal control is yielded. A generalization of the approach illustrated by these results to control problems on arbitrary Abelian Lie groups is included.
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