Sound Compilation of Weighted Event Signal Temporal Logic to Timeless Geometric Control

RESUMO

Cyber-Physical Systems (CPS) controllers synthesized from standard temporal logics rely on rigid global clocks, rendering them vulnerable to asynchronous timing anomalies like clock snaps, jitter, and network delays. To overcome these vulnerabilities, we introduce a fundamentally timeless geometric control paradigm alongside a novel specification language: Weighted Event-Based Signal Temporal Logic (weSTL+). This new weSTL+ logic combines the event triggered nature of Event-STL with weighted user preferences of weighted-STL making it suitable for specification of practical autonomous CPS. Using a two-pass compiler, our framework translates weSTL+ formulae directly into C^1-differentiable time-invariant geometric surrogate constraints via finite-time level-set inversion. By mapping temporal windows directly into physical time independent geometric boundaries, this approach entirely eliminates explicit runtime clock monitoring. Our autonomous robotics case study demonstrates that the proposed geometric architecture guarantees enforcement of safety and liveness under severe macroscopic timing discontinuities, succeeding where traditional time-indexed controllers fail.