We consider exact and averaged control problem for a system of quasilinear ODEs and SDEs with a nonnegative 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).

中文翻译：

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ODE 和 SDE 拟线性非负定系统的全局可控性

我们考虑具有系统非负定对称矩阵的拟线性 ODE 和 SDE 系统的精确和平均控制问题。证明的策略是通过固定出现在系统非线性部分的函数，然后应用 Leray-Schauder 不动点定理对系统进行标准线性化。我们还需要连续归纳论证来将控制延长到最终状态，这是该领域的一种新方法。这使我们能够获得对任意大的初始数据的可控性（所谓的全局可控性）。