论文标题
仿射无漂移系统的磁滞和可控性：一些案例研究
Hysteresis and controllability of affine driftless systems: some case studie
论文作者
论文摘要
我们研究了某些无漂移仿射系统的可控性，在这些系统中考虑了控制效果，包括在控制和状态进化中。特别是我们考虑两种情况：一种情况：一种均由所谓的游戏操作员代表的磁滞，而一种均由所谓的延迟继电器代表的情况。在第一种情况下，我们证明，在某些假设下，每当相应的非滞后系统是可控制的，那么我们也至少可以大致控制滞后。这是通过一些适当构建的磁滞操作员输入的近似值获得的。在第二种情况下，我们证明了通用滞后延迟开关系统的可控性。最后，我们研究了两种情况之间的一些可能的连接。
We investigate the controllability of some kinds of driftless affine systems where hysteresis effects are taken into account, both in the realization of the control and in the state evolution. In particular we consider two cases: the one when hysteresis is represented by the so-called play operator, and the one when it is represented by a so-called delayed relay. In the first case we prove that, under some hypotheses, whenever the corresponding non-hysteretic system is controllable, then we can also, at least approximately, control the hysteretic one. This is obtained by some suitably constructed approximations for the inputs in the hysteresis operator. In the second case we prove controllability for a generic hysteretic delayed switching system. Finally, we investigate some possible connections between the two cases.
