论文标题
双连续半群的最终状态可观察性估计和成本均匀的近似近似可控性
Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups
论文作者
论文摘要
我们考虑了BANACH空间上双连续半群的最终状态可观察性估计值，即，对于每个初始值，通过考虑到适当规范的[0，T] $的$ t \ in [0，t] $的$ t \ in [0，t] $的$ t \下的初始值的轨道来估计状态$ t> 0 $。我们根据不确定性关系和耗散估计，提供了足够的标准，并提供了两个共同连续的半群的例子，这些示例具有最终的状态可观察性估计值，即高斯 - 韦尔斯特拉斯半群和Ornstein-uhlenbeck semogep在有限持续功能的空间上。此外，我们将成本均匀的近似可控性与最终状态可观察性估计之间的二元性概括为局部凸出空间的设置，以构成有限和连续的控制功能，即使对于Banach空间案例，这似乎是新的。
We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time $T>0$ by taking into account the orbit of the initial value under the semigroup for $t\in [0,T]$, measured in a suitable norm. We state a sufficient criterion based on an uncertainty relation and a dissipation estimate and provide two examples of bi-continuous semigroups which share a final state observability estimate, namely the Gauss-Weierstrass semigroup and the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions. Moreover, we generalise the duality between cost-uniform approximate null-controllability and final state observability estimates to the setting of locally convex spaces for the case of bounded and continuous control functions, which seems to be new even for the Banach spaces case.
