STLCCP: Efficient Convex Optimization-Based Framework for Signal Temporal Logic Specifications

• 成果类型: Article
• 署名作者: Takayama, Yoshinari; Hashimoto, Kazumune; Ohtsuka, Toshiyuki
• 署名单位: Universite Paris Saclay; University of Osaka; Kyoto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3555949
• 发表日期: 2025
• 页码: 6064-6079
• 关键词: robustness; logic; optimization; Convex functions; trajectory; Time-domain analysis; Syntactics; STANDARDS; Smoothing methods; scalability; Convex Optimization; formal methods; optimal control; signal temporal logic (STL)

摘要

Signal temporal logic (STL) is a powerful formalism for specifying various temporal properties in dynamical systems. However, existing methods, such as mixed-integer programming and nonlinear programming, often struggle to efficiently solve control problems with complex, long-horizon STL specifications. This study introduces STLCCP, a novel convex optimization-based framework that leverages key structural properties of STL: monotonicity of the robustness function, its hierarchical tree structure, and correspondence between convexity/concavity in optimizations and conjunctiveness/ disjunctiveness in specifications. The framework begins with a structure-aware decomposition of STL formulas, transforming the problem into an equivalent difference of convex programs. This is then solved sequentially as a convex quadratic program using an improved version of the convex-concave procedure. To further enhance efficiency, we develop a smooth approximation of the robustness function using a function termed the mellowmin function, specifically tailored to the proposed framework. Numerical experiments on motion planning benchmarks demonstrate that STLCCP can efficiently handle complex scenarios over long horizons, outperforming existing methods.