Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic

2026-07-09

AI Summary

This work addresses the challenge of synthesizing parameters for nonlinear systems under uncertain initial conditions to satisfy continuous-time Signal Temporal Logic (STL) specifications. The authors propose a novel approach that integrates gradient-based optimization with set-based reachability verification, uniquely combining learnable optimization and formal verification. This integration enables efficient exploration of high-dimensional parameter spaces while providing rigorous guarantees of robust satisfaction of STL specifications. The method is evaluated on three nonlinear systems, demonstrating both effectiveness and scalability by successfully handling parameter spaces up to 18 dimensions and delivering formally verifiable correctness assurances.

Abstract

Signal Temporal Logic (STL) is increasingly used to describe interpretable objectives and constraints for optimal control and learning methods, especially when no target time series data is available. In this work, we propose to synthesize parameters for nonlinear systems that robustly satisfy continuous-time STL specifications for uncertain initial conditions. To this end, we use gradient-based optimization along with set-based reachability verification to efficiently learn in high-dimensional parameter spaces while providing provable satisfaction guarantees for the optimized parameters. We demonstrate the effectiveness and scalability of our method on three systems with up to 18 parameter dimensions.

Problem

• parameter synthesis
• nonlinear systems
• Signal Temporal Logic
• robust satisfaction
• uncertain initial conditions

Innovation

• Signal Temporal Logic
• Parameter Synthesis
• Reachability Verification
• Gradient-based Optimization
• Nonlinear Systems