控制问题和控制和受控轨迹上的线性投影约束
Control issues and linear projection constraints on the control and on the controlled trajectory
摘要：
本文的目的是讨论形式为$y' = Ay + Bu$的抽象线性系在控制$u$或/和受控轨迹$y$上的一些附加线性投影约束下的能控性。特别是，我们讨论的可能性施加的线性投影的控制轨迹和控制，在近似可控性，精确可控性和零可控性的背景下。事实证明，在所有这些设置中，为了能够对轨迹和控制施加线性投影约束，我们将强烈依赖于伴随系统的唯一连续性质，据我们所知，迄今为止尚未确定，并且似乎不是经典的。因此，我们将提供几个例子，在这些例子中，可以检验这个唯一的连续性。
英文摘要：
The goal of this article is to discuss controllability properties for an abstract linear system of the form $y' = Ay + Bu$ under some additional linear projection constraints on the control $u$ or / and on the controlled trajectory $y$. In particular, we discuss the possibility of imposing the linear projections of the controlled trajectory and of the control, in the context of approximate controllability, exact controllability and null-controllability. As it turns out, in all these settings, for being able to impose linear projection constraints on the trajectory and on the control, we will strongly rely on a unique continuation property for the adjoint system which, to our knowledge, has not been identified so far, and which does not seem classical. We shall therefore provide several instances in which this unique continuation property can be checked.
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