论文标题
线性时间延迟方程的最小能量确切的无效可控性问题
Minimum energy exact null-controllability problem for linear time-delay equations
论文作者
论文摘要
我们研究具有点延迟的微分方程的最小能量可控性问题。对于中性和智障类型的方程式，我们将找到最佳控制的问题减少到Volterra积分方程并明确求解。我们证明，对于任何初始状态和任何可控时间，相应的最佳控件属于方程指数产生的特征空间。此外，我们表明所提出的方法可以应用于具有一个延迟期限的延迟方程系统。
We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral equation and solve it explicitly. We prove that for any initial state and any controllability time the corresponding optimal control belongs to the characteristic space generated by the equation's exponentials. Besides, we show that the proposed approach can be applied to the systems of retarded equations with one delay term.
