Real-Time Synthesis of Robust Controlled Invariant Sets for Monotone Systems

2026-09-12

AI Summary

针对安全关键控制中不变集在线计算难题，提出一种基于阈值函数重构的方法，实现高效并行计算，大幅降低计算复杂度。

Abstract

Safety-critical control of autonomous systems requires formal safety certificates, such as controlled invariant sets, that must be computed online as conditions change. Although standard synthesis algorithms scale poorly with state dimension, monotone dynamical systems with lower-closed safety specifications allow for accelerated computation of controlled invariant sets. In particular, lazy fixed-point algorithms exploit monotonicity and track only the antichain basis of the set. However, membership tests and redundancy checks against an evolving basis remain major bottlenecks. We introduce a threshold-function reformulation in which a lower-closed set on a d-dimensional grid is represented by its column heights along a designated axis. This reformulates the greatest-fixed-point iteration as independent one-dimensional binary searches, one per grid column, yielding an embarrassingly parallel iteration with asymptotically lower computational complexity than the lazy fixed-point algorithm. Experiments synthesize invariant sets on 3D grids with 10^9 cells in under 50 ms and 10^14 cells in under two minutes. We further demonstrate online re-synthesis in a safety-informed model predictive controller example.

Problem

• safety-critical control
• controlled invariant sets
• monotone systems
• online computation
• computational complexity

Innovation

• threshold-function reformulation
• embarrassingly parallel iteration
• lower computational complexity