提出时空鲁棒性新框架,兼顾空间与时间扰动的协同分析。
Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning
- 将时空鲁棒性建模为多目标优化问题,通过偏序关系统一刻画空间与时间扰动。
- 定义可计算的稳健语义,能在保证安全的前提下高效求解鲁棒性边界。
- 适用于多智能体机器人、智慧交通等需协同决策的复杂系统。
自主系统的可靠性依赖于其在不确定性下的鲁棒性,即在扰动下仍能达成目标的能力。本文研究离散时间信号上时序逻辑规范的时空鲁棒性。现有工作提出了仅考虑空间扰动的鲁棒语义,能捕捉距离不满足的几何距离。本文提出时空鲁棒性(STR),同时建模空间与时间扰动的联合影响。该概念对多智能体机器人、智慧城市和空中交通管制等交互系统尤为关键。我们将STR形式化为多目标推理问题,基于空间与时间扰动的偏序关系。该视角具有两大优势:(1) STR可解释为帕累托最优集,表征所有可接受的时空扰动;(2) 可利用多目标优化工具进行计算。为应对计算挑战,我们提出保真且可计算的稳健语义,能合理下近似STR。最后,我们设计了基于这些语义的监控算法。据我们所知,这是首个通过多目标推理处理多维鲁棒性的研究。
原文摘要 · Abstract (English)
The reliability of autonomous systems depends on their robustness, i.e., their ability to meet their objectives under uncertainty. In this paper, we study spatiotemporal robustness of temporal logic specifications evaluated over discrete-time signals. Existing work has proposed robust semantics that capture not only Boolean satisfiability, but also the geometric distance from unsatisfiability, corresponding to admissible spatial perturbations of a given signal. In contrast, we propose spatiotemporal robustness (STR), which captures admissible spatial and temporal perturbations jointly. This notion is particularly informative for interacting systems, such as multi-agent robotics, smart cities, and air traffic control. We define STR as a multi-objective reasoning problem, formalized via a partial order over spatial and temporal perturbations. This perspective has two key advantages: (1) STR can be interpreted as a Pareto-optimal set that characterizes all admissible spatiotemporal perturbations, and (2) STR can be computed using tools from multi-objective optimization. To navigate computational challenges, we propose robust semantics for STR that are sound in the sense of suitably under-approximating STR while being computationally tractable. Finally, we present monitoring algorithms for STR using these robust semantics. To the best of our knowledge, this is the first work to deal with robustness across multiple dimensions via multi-objective reasoning.
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