信号时序逻辑遇上凸凹规划：一种针对STL规范的利用结构特性的SQP算法
Signal Temporal Logic Meets Convex-Concave Programming: A Structure-Exploiting SQP Algorithm for STL Specifications
AI总结：
针对带STL规范的控制问题中现有SQP方法易陷局部极小值的缺陷，提出基于CCP的结构利用型SQP算法，通过鲁棒性分解构造DC规划并仅近似析取部分求解，在鲁棒性和计算时间上均优于现有方法。
摘要：
本研究针对带信号时序逻辑（signal temporal logic, STL）规范的控制问题展开。现有研究采用平滑技术以在可行时间内求解该问题，并直接套用序列二次规划（sequential quadratic programming, SQP）方法求解，但该方法的缺陷之一是解容易陷入不满足规范的局部极小值。本研究提出一种基于凸凹过程（convex-concave procedure, CCP）的新型优化方法，命名为CCP-based SQP。该框架包含一种全新的鲁棒性分解方法，可将鲁棒性函数分解为一组约束，最终形成可高效求解的凸差（difference of convex, DC）规划形式。我们仅通过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，该方法在鲁棒性和计算时间两方面，均优于当前最先进的SQP方法。
英文摘要：
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.
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