Fast Constraint Extraction for Corrective Control under STL Specifications via Logical Dependency Tracking

2026-09-08

AI Summary

本文通过逻辑依赖跟踪框架解决在不确定性下满足STL规范的问题，使用三值语义传播不确定性并提取约束条件，进而通过线性规划实现控制校正。

Abstract

Ensuring the satisfaction of Signal Temporal Logic (STL) specifications under uncertainty is challenging, as reachability-based monitoring provides guarantees but does not indicate how to restore satisfaction when it becomes indeterminate. A key difficulty is identifying which uncertain components actually affect global satisfaction, especially for nested formulas. This paper introduces a logical dependency tracking framework that propagates uncertainty through the STL structure and captures the causal contribution of reachable sets to satisfaction. By associating markers to uncertain predicates and propagating them via three-valued semantics, we extract in milliseconds a compact Disjunctive Normal Form (DNF) of sufficient constraints, avoiding combinatorial enumeration. As an application, we formulate control correction as a minimum-effort optimization problem. Using zonotopic reachability, the derived constraints are enforced via linear programming, yielding corrections that guarantee STL satisfaction under bounded uncertainty and provide certified probabilistic bounds in the stochastic case. We demonstrate the approach on a nonlinear system with nested STL specifications, showing that dependency tracking enables efficient and formally guaranteed correction. The tracking implementation is available at https://github.com/Antoine-Bst/STL-Three-Valued-Clause-Filtering/.

Problem

• Signal Temporal Logic
• uncertainty
• reachability-based monitoring
• nested formulas
• global satisfaction

Innovation

• Logical Dependency Tracking
• Three-Valued Semantics
• Disjunctive Normal Form (DNF)
• Zonotopic Reachability
• Linear Programming