论文标题
半线性部分微分方程的线性可控性分析
Linearized Controllability Analysis of Semilinear Partial Differential Equations
论文作者
论文摘要
众所周知，可以通过显示线性化系统的可控性来确定有限维非线性系统的可控性。但是，这种经典结果并未推广到无限二二维非线性系统。在本文中，我们将自己限制在半线性的无限维系统中，并表明线性化系统的确切可控性意味着非线性系统的确切可控性。关于非线性操作员的限制与有关半线性系统线性化稳定性分析的文献中可以找到的限制相似。
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional nonlinear systems. In this paper, we restrict ourselves to semilinear infinite-dimensional systems, and show that the exact controllability of the linearized system implies exact controllability of the nonlinear system. The restrictions concerning the nonlinear operator are similar to those that can be found in the literature about the linearized stability analysis of semilinear systems.
