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首页> 外文期刊>SIAM Journal on Control and Optimization >Boundary controllability of the Korteweg-de Vries equation on a bounded domain
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Boundary controllability of the Korteweg-de Vries equation on a bounded domain

机译：有界域上Korteweg-de Vries方程的边界可控性

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This paper studies boundary controllability of the Korteweg-de Vries equation posed on a finite interval, in which, because of the third-order character of the equation, three boundary conditions are required to secure the well-posedness of the system. We consider the cases where one, two, or all three of those boundary data are employed as boundary control inputs. The system is first linearized around the origin and the corresponding linear system is proved to be exactly boundary controllable if using two or three boundary control inputs. In the case where only one control input is allowed to be used, the linearized system is known to be only null controllable if the single control input acts on the left end of the spatial domain. By contrast, if the single control input acts on the right end of the spatial domain, the linearized system is shown to be exactly controllable if and only if the length of the spatial domain does not belong to a set of critical values. Moreover, the nonlinear system is shown to be locally exactly boundary controllable via the contraction mapping principle if the associated linearized system is exactly controllable.
机译：本文研究了有限区间上的Korteweg-de Vries方程的边界可控性，其中，由于方程的三阶特征，需要三个边界条件来保证系统的适定性。我们考虑将其中一个，两个或所有三个边界数据用作边界控制输入的情况。该系统首先围绕原点进行线性化，并且如果使用两个或三个边界控制输入，则证明相应的线性系统是完全边界可控制的。在仅允许使用一个控制输入的情况下，如果单个控制输入作用于空间域的左端，则线性化系统仅是空可控的。相反，如果单个控制输入作用于空间域的右端，则当且仅当空间域的长度不属于一组临界值时，线性化系统才显示为可精确控制的。此外，如果相关联的线性化系统是可精确控制的，则非线性系统通过收缩映射原理显示为局部可精确边界控制。

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