Methods of Control Theory in Nonholonomic Geometry

LetM be a C∞-manifold andTM the total space of the tangent bundle. A control system is a subset V ⊂ TM. Fix an initial point q0 ∈ M and a segment [0,t] ⊂ ℝ. Admissible trajectories are Lipschitzian curves q(τ), 0 ≤ τ ≤ t, q(0) = q0 satisfying a differential equation of the form where is smooth in bounded and measurable in T. The mapping which maps admissible trajectories in their end points, is called an end-point mapping.