This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential quadratic programming (SQP) methods naively. However, one of the drawbacks of this approach is that solutions can easily become trapped in local minima that do not satisfy the specification. In this study, we propose a new optimization method, termed CCP-based SQP, based on the convex-concave procedure (CCP). Our framework includes a new robustness decomposition method that decomposes the robustness function into a set of constraints, resulting in a form of difference of convex (DC) program that can be solved efficiently. We solve this DC program sequentially as a quadratic program by only approximating the disjunctive parts of the specifications. Our experimental results demonstrate that our method has a superior performance compared to the state-of-the-art SQP methods in terms of both robustness and computational time.

翻译：本研究考虑带有信号时序逻辑（STL）规范的控制问题。先前的工作采用平滑技术以在可行时间范围内解决该问题，并通过朴素应用序列二次规划（SQP）方法对其进行求解。然而，该方法的一个缺陷在于解容易陷入不满足规范要求的局部极小值。本文基于凸-凹过程（CCP），提出一种名为"基于CCP的序列二次规划"的新型优化方法。我们的框架包含一种新的鲁棒性分解方法，该方法将鲁棒性函数分解为一组约束，从而形成可高效求解的凸函数差（DC）规划形式。我们通过仅近似规范中的析取部分，将该DC规划作为二次规划进行序列求解。实验结果表明，相较于现有最优的SQP方法，本文方法在鲁棒性和计算时间两方面均展现出更优性能。