Constrained approximate null controllability of coupled heat equation with periodic impulse controls
Constrained approximate null controllability of coupled heat equation with periodic impulse controls
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发表时间：
2020-05
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通讯作者：
Lijuan Wang;Qishu Yan;Huaiqiang Yu
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作者：
Lijuan Wang;Qishu Yan;Huaiqiang Yu
本文研究了热传导方程与实矩阵耦合的约束近似零能控性，其中控制是脉冲的，并通过一系列实矩阵作用于系统。给出了两种情况下的结论。在控制全局作用于系统的情况下，我们证明了在谱条件为$P$、秩条件为$P$和q_k=1的情况下，系统是全局约束近似零可控的；而当控制作用于系统的局部时，我们证明了在更强的条件下以及与上述情形相同的秩条件下，系统是全局约束近似零可控的。此外，我们还证明了上述谱条件是本文所考虑的控制问题全局约束近似零能控性的必要条件。
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.