🤖 AI Summary
This work addresses the optimal control problem under long-horizon signal temporal logic (STL) constraints, where conventional mixed-integer/nonlinear programming (MIP/NLP) approaches suffer from low efficiency and poor real-time tractability for complex STL specifications. We propose a structure-aware STL decomposition strategy that enables, for the first time, STL syntax-driven difference-of-convex (DC) modeling. Integrating the convex–concave procedure (CCP) with sequential convex quadratic programming (QP), our method transforms the original NP-hard problem into a scalable, real-time-solvable DC program. This yields significant improvements in computational speed and solution feasibility. In extensive benchmark evaluations, our approach successfully solves long-horizon, high-complexity STL control tasks that are intractable for standard MIP/NLP solvers—achieving, for the first time, real-time STL control synthesis.
📝 Abstract
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 extit{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.