SIAM Journal on Control and Optimization, Volume 58, Issue 1, Page 425-446, January 2020.
In this paper, we study small-time local controllability of real analytic control-affine systems under small perturbations of their vector fields. Consider a real analytic control system X which is small-time locally controllable and whose reachable sets shrink with the polynomial rate of order N with respect to time. We will prove a general theorem which states that any real analytic control-affine system whose vector fields are perturbations of the vector fields of X with polynomials of order higher than N is again small-time locally controllable. In particular, we show that this result connects two long-standing open conjectures about small-time local controllability of systems.

中文翻译：

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小型本地可控性

SIAM控制与优化杂志，第58卷，第1期，第425-446页，2020
年1月。在本文中，我们研究了在矢量场的微小扰动下实际解析控制仿射系统的小局部局部可控性。考虑一个真正的解析控制系统X，该系统可以在短时间内进行局部控制，并且其可到达集合相对于时间以N阶多项式速率收缩。我们将证明一个一般性定理，该定理指出，向量场是X的向量场的扰动且阶次大于N的多项式的任何实际解析控制仿射系统都可以在短时间内进行局部控制。特别是，我们证明了该结果将两个长期存在的关于系统的局部局部可控性的开放猜想联系在一起。