In this article, we formulate the problem of satisfying a linear temporal logic formula on a linear plant with output feedback, through a recent hybrid systems formalism. We relate this problem to the notion of recurrence introduced for the considered formalism, and we then extend Lyapunov-like conditions for recurrence of an open, unbounded set. One of the proposed relaxed conditions allows certifying recurrence of a suitable set, and this guarantees that the high-level evolution of the plant satisfies the formula, without relying on discretizations of the plant. Simulations illustrate the proposed approach.

中文翻译：

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通过混合系统的递归工具满足线性时态逻辑规范


在本文中，我们通过最近的混合系统形式体系，提出了在具有输出反馈的线性设备上满足线性时序逻辑公式的问题。我们将这个问题与为所考虑的形式主义引入的递归概念联系起来，然后我们将类似李雅普诺夫的条件扩展到开放无界集的递归。所提出的宽松条件之一允许证明合适集合的重现，这保证了植物的高级进化满足公式，而不依赖于植物的离散化。模拟说明了所提出的方法。