论文标题
分析性分析和应用到抛物线系统的转换控件
Switching Controls for Analytic Semigroups and Applications to Parabolic Systems
论文作者
论文摘要
在这项工作中，我们进一步推动了[E. Zuazua，Switching Control，J。Eur。数学。 Soc。 （JEMS），13（1）：85--117，2011]。问题在于以下一个：假设一个人可以使用两个或多个执行器控制系统，是否存在一种控制策略，以至于任何时候，只有一个执行器是活跃的？当受控系统对应于由积极的自动接合操作员跨越的分析半群时，我们对这个问题进行了积极回答，该分析系统在任意的小时间内可无效。与Zuazua大肠杆菌的论点类似，我们的证明依赖于分析性论点，并且在操作员跨越分析半群时，不一定是自我关节时，也将在有限的维度设置中起作用。
In this work, we push further the analysis of the problem of switching controls proposed in [E. Zuazua, Switching control, J. Eur. Math. Soc. (JEMS), 13(1): 85--117, 2011]. The problem consists in the following one: assuming that one can control a system using two or more actuators, does there exist a control strategy such that at all times, only one actuator is active? We answer positively to this question when the controlled system corresponds to an analytic semigroup spanned by a positive self-adjoint operator which is null-controllable in arbitrary small times. Similarly as the argument of E. Zuazua, our proof relies on analyticity arguments and will also work in finite dimensional setting and under some further spectral assumptions when the operator spans an analytic semigroup but is not necessarily self-adjoint.
