High Order Algebraic Conditions for Controllability

摘要: Let X,Y2,...,Ym be analytic vector fields on an analytic, n — dimensional, manifold M, and ϑ the control system $$\mathop x\limits^. = X(x) + \sum\nolimits_{i 2}^m {{u_i}(t){Y^i}(x),x(o) p \in M,(\mathop dx/dt)} $$ (1) where, unless stated otherwise, admissible is a Lebesgue measurable function u with components |ui(t)| ≤ 1. a(t,p, ϑ) will denote set of all points attainable at time t ≥ 0 by solutions corresponding to controls; TX (•)p solution . Our problem determine necessary sufficient conditions that TX(t)p ∈ int. ∀t >