Optimal inner-product angular momentum controllers

An optimization technique is presented to reduce to zero the angular velocities of a spinning object while minimizing a general performance criterion. Closed-form control laws are obtained for a controller structure with a single nonlinear transducer in the feedback loop that employs the square of the Euclidean distance to the origin as an error signal. Consideration is also given to the "inverse problem" of optimal control. Linearization and generalization of the nonlinear plant are discussed.