论文标题
与周期性脉冲控制的耦合热方程的约束近似无效的可控性
Constrained approximate null controllability of coupled heat equation with periodic impulse controls
论文作者
论文摘要
本文涉及加热方程的约束近似无效的可控性，结合了真实矩阵$ p $，其中控件是冲动的，并通过一系列真实矩阵$ \ {q_k \} _ {k = 1}^\ hbar $通过一系列真实矩阵$ \ {q_k \} _ {q_k \} _ {q_k \} _ {q_k \} _ {q_k \} _ {结论在两种情况下给出。如果控件在全球范围内作用于系统，我们证明该系统在$ p $的频谱条件下被全局约束近似null可控，而排名条件为$ p $和$ \ {q_k \} _ {k = 1}^\ hbar $;尽管控件在本地作用于系统中，但我们证明了在$ p $的强度较强的情况下，全局约束的近似null可控性和与上述情况相同的等级条件。此外，我们证明，上述$ p $的光谱条件对于本文考虑的控制问题的全局约束近似无效可控性是必需的。
This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix $P$, where the controls are impulsive and periodically acted into the system through a series of real matrices $\{Q_k\}_{k=1}^\hbar$. The conclusions are given in two cases. In the case that the controls act globally into the system, we prove that the system is global constrained approximate null controllable under a spectral condition of $P$ together with a rank condition of $P$ and $\{Q_k\}_{k=1}^\hbar$; While in the case that the controls act locally into the system, we prove the global constrained approximate null controllability under a stronger condition for $P$ and the same rank condition as the above case. Moreover, we prove that the above mentioned spectral condition of $P$ is necessary for global constrained approximate null controllability of the control problem considered in this paper.
