This work addresses maximally robust control synthesis under unknown disturbances. We consider a general nonlinear system, subject to a Signal Temporal Logic (STL) specification, and wish to jointly synthesize the maximal possible disturbance bounds and the corresponding controllers that ensure the STL specification is satisfied under these bounds. Many works have considered STL satisfaction under given bounded disturbances. Yet, to the authors' best knowledge, this is the first work that aims to maximize the permissible disturbance set and find the corresponding controllers that ensure satisfying the STL specification with maximum disturbance robustness. We extend the notion of disturbance-robust semantics for STL, which is a property of a specification, dynamical system, and controller, and provide an algorithm to get the maximal disturbance robust controllers satisfying an STL specification using Hamilton-Jacobi reachability. We show its soundness and provide a simulation example with an Autonomous Underwater Vehicle (AUV).

翻译：本文研究未知扰动下的最大稳健控制综合问题。我们考虑受信号时序逻辑（STL）约束的一般非线性系统，旨在联合求解最大可能的扰动界以及能够保证在这些扰动界下满足STL规范的相应控制器。已有大量工作研究了给定有界扰动下的STL满足性问题，然而据作者所知，本文首次致力于最大化允许的扰动集合，并寻找能确保在最大扰动鲁棒性下满足STL规范的相应控制器。我们扩展了STL的扰动鲁棒语义概念（该概念是规范、动力系统与控制器的共同性质），并提出一种算法，利用Hamilton-Jacobi可达性分析获取满足STL规范的最大扰动鲁棒控制器。我们证明了算法的正确性，并以自主水下航行器（AUV）为例进行了仿真验证。