标题： 符号控制：揭示自由鲁棒性裕度 显示英文标题

标题： Symbolic Control: Unveiling Free Robustness Margins

摘要： 本文解决了在存在系统扰动的情况下，确保符号控制技术鲁棒性的挑战。 给定一个离散时间控制系统，其与符号模型之间通过交替模拟关系相关联。 在本文中，我们专注于计算最大鲁棒性边界，在此边界下，符号模型对于离散时间控制系统的扰动版本仍然有效。 我们首先表明，符号模型本质上具备一定的自由鲁棒性边界。 然后，我们提供构造性方法来计算一致的和非一致的（状态和输入依赖的）鲁棒性边界。 我们还表明，鲁棒性边界的紧致性取决于用于计算符号模型的可达性技术的紧致性。 随后，我们解释如何利用计算得到的鲁棒性边界进行控制器综合。 最后，我们提供了两个示例来展示我们方法的有效性。 显示英文摘要

摘要： This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related to its symbolic model by an alternating simulation relation. In this paper, we focus on computing the maximum robustness margin under which the symbolic model remains valid for a perturbed-version of the discrete-time control system. We first show that symbolic models are inherently equipped with a certain free robustness margins. We then provide constructive procedures to compute uniform and non-uniform (state and input dependent) robustness margins. We also show that the tightness of the robustness margin depends on the tightness of the reachability technique used to compute the symbolic model. We then explain how the computed robustness margin can be used for the sake of controller synthesis. Finally, we present two illustrative examples to demonstrate the effectiveness of our approach.