Certain Controllability Properties of Analytic Control Systems

In this article we consider analytic control systems defined on an analytic manifold M. In particular, we study the relationship between the accessibility property, i.e., attainable sets having nonempty interior, and controllability. This study is restricted to analytic control systems because they admit a very simple algebraic criterion for determining the accessibility property; this criterion is a generalization of the well-known rank condition for linear systems. The main difficulty in extending the accessibility property to yield controllability lies in the fact that the time coordinate is nondecreasing. Beside systems of the form $F(x,u) = - F(x, - u)$, right invariant control systems defined on a compact Lie group are controllable whenever they have the accessibility property. It seems reasonable that a similar result should hold for arbitrary compact manifolds.