Signal Temporal Logic (STL) is capable of expressing a broad range of temporal properties that controlled dynamical systems must satisfy. In the literature, both mixed-integer programming (MIP) and nonlinear programming (NLP) methods have been applied to solve optimal control problems with STL specifications. However, neither approach has succeeded in solving problems with complex long-horizon STL specifications within a realistic timeframe. This study proposes a new optimization framework, called \textit{STLCCP}, which explicitly incorporates several structures of STL to mitigate this issue. The core of our framework is a structure-aware decomposition of STL formulas, which converts the original program into a difference of convex (DC) programs. This program is then solved as a convex quadratic program sequentially, based on the convex-concave procedure (CCP). Our numerical experiments on several commonly used benchmarks demonstrate that this framework can effectively handle complex scenarios over long horizons, which have been challenging to address even using state-of-the-art optimization methods.

翻译：信号时序逻辑（STL）能够表达受控动态系统必须满足的广泛时序性质。现有文献中，混合整数规划（MIP）和非线性规划（NLP）方法均已被应用于求解带有STL规范的最优控制问题。然而，这两种方法都未能成功在合理时间范围内解决具有复杂长时域STL规范的问题。本研究提出一种名为\textit{STLCCP}的新型优化框架，该框架显式地利用了STL的若干结构特性以缓解这一问题。我们框架的核心是一种结构感知的STL公式分解方法，它将原始问题转化为凸函数之差（DC）规划。随后，基于凸凹过程（CCP），该规划被转化为一系列凸二次规划进行求解。在若干常用基准测试上的数值实验表明，该框架能够有效处理长时域上的复杂场景，而这些问题即使使用最先进的优化方法也极具挑战性。