论文标题
最佳时间内双曲系统的无效控制性，确切的可控性和稳定性
Null-controllability, exact controllability, and stabilization of hyperbolic systems for the optimal time
论文作者
论文摘要
在本文中，我们讨论了有关零可控性，确切可控性和在一维空间中使用边界控件在一侧的一侧的稳定性的稳定性，以最佳时间为止。在另一侧的边界条件上的精确和通用假设下，我们首先获得了无效的最佳时间，并为这些系统提供了通用源项的确切可控性。然后，我们证明了无效的可控制性和确切的可控性，任何时间都比最佳时间和任何源术语。最后，对于同质系统，我们设计了稳定系统并将它们在最佳时间将其带到零状态的反馈。还讨论了非线性同质系统的扩展
In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under precise and generic assumptions on the boundary conditions on the other side, we first obtain the optimal time for the null and the exact controllability for these systems for a generic source term. We then prove the null-controllability and the exact controllability for any time greater than the optimal time and for any source term. Finally, for homogeneous systems, we design feedbacks which stabilize the systems and bring them to the zero state at the optimal time. Extensions for the non-linear homogeneous system are also discussed
