When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. This may lead to some unwanted chattering effects than may damage the system. This behavior is difficult to observe even in simulation. In this paper, we propose an interval approach to characterize the sliding surface which corresponds to the set of all states such that the state trajectory may jump indefinitely between two distinct behaviors. We show that the recent notion of thick sets will allows us to compute efficiently an outer approximation of the sliding surface of a given class of hybrid system taking into account all set-membership uncertainties. An application to the verification of the controller of a child swing is considered to illustrate the principle of the approach.

中文翻译：

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封闭受控秋千的滑动表面

当为电子物理系统实现非连续控制器时，可能会发生闭环系统的演化不再沿着轨迹逐段微分的情况，这主要是由于控制器内部的条件语句所致。这可能会导致一些不必要的颤动效果，而不是损坏系统。即使在仿真中也很难观察到此行为。在本文中，我们提出了一种区间方法来表征与所有状态集相对应的滑动表面，从而使状态轨迹可以在两个不同的行为之间无限期地跳跃。我们表明，最近的厚集概念将使我们能够有效地计算给定类别的混合系统的滑移面的外部近似，同时考虑到所有集成员资格的不确定性。