Feedback decoupling of rotational disturbances for spherically constrained systems

In this paper, the problem of decoupling rotational disturbances, using (nonlinear) state feedback, from the output of a scalar system evolving on a sphere is posed and solved. The techniques employed require a further development of the emerging nonlinear generalization of the linear geometric control theory, pioneered by Basile-Marro and by Wonham-Morse. The existing nonlinear results concentrate on local issues and are valid under hypotheses requiring sufficient regularity in the problem data. The novel developments contained in this paper are required by the presence of local singularities in the problem data and by the global nature of the problem. Perhaps surprisingly, after a "resolution of singularities" of the appropriate foliations, the local singular problem is shown to be equivalent to a global nonsingular problem. These global problems are then solved using standard methods from algebraic and differential topology.