We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system, and then applying the Leray-Schauder fixed point theorem. We shall also need the continuous induction arguments to prolong the control to the final state which is a novel approach in the field. This enables us to obtain controllability for arbitrarily large initial data (so called global controllability).

翻译：我们考虑的是一个具有系统非负线性确定对称矩阵的准线性极数和SDE系统的精确和平均控制问题。 证明策略是确定系统非线性部分的功能,然后应用 Leray-Schauder 固定点的定点理论,从而确定系统的标准线性。 我们还需要连续的上岗论证,将控制扩展至最后一个状态,这是这个领域的一种新办法。 这使得我们能够获得任意的大型初始数据的可控性( 所谓的全球可控性 ) 。