拟线性非负定常、偏微分方程组的全局能控性
Global Controllability for Quasilinear Non-negative Definite System of ODEs and SDEs
摘要：
考虑一类拟线性常微分方程组和具有非负定对称矩阵的随机微分方程组的精确平均控制问题。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，将系统标准线性化。我们还需要连续的归纳论点，以延长控制的最终状态，这是一个新的方法在该领域。这使我们能够获得任意大的初始数据的可控性（所谓的全局可控性）。
英文摘要：
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).
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