Minimal Information Control Invariance via Vector Quantization

2026-04-03

AI Summary

This work addresses the challenge of preserving state constraint invariance in safety-critical systems under stringent computational and perceptual resource limitations, using minimal control signaling. The authors propose a certifiable safety-aware control compression framework that uniquely integrates information-theoretic invariance entropy with control codebook minimization. By jointly learning a partition of the state space and a finite control codebook via a vector-quantized autoencoder, and combining Lipschitz-based reachability set estimation with sum-of-squares programming, the method iteratively verifies forward invariance of the closed-loop system. Evaluated on a 12-dimensional nonlinear quadrotor model, the approach achieves a 157× reduction in codebook size compared to a uniform-grid baseline while rigorously maintaining set invariance, and quantifies the minimum perceptual resolution required for safe operation.

Abstract

Safety-critical autonomous systems must satisfy hard state constraints under tight computational and sensing budgets, yet learning-based controllers are often far more complex than safe operation requires. To formalize this gap, we study how many distinct control signals are needed to render a compact set forward invariant under sampled-data control, connecting the question to the information-theoretic notion of invariance entropy. We propose a vector-quantized autoencoder that jointly learns a state-space partition and a finite control codebook, and develop an iterative forward certification algorithm that uses Lipschitz-based reachable-set enclosures and sum-of-squares programming. On a 12-dimensional nonlinear quadrotor model, the learned controller achieves a $157\times$ reduction in codebook size over a uniform grid baseline while preserving invariance, and we empirically characterize the minimum sensing resolution compatible with safe operation.

Problem

• control invariance
• information efficiency
• safety-critical systems
• sampled-data control
• invariance entropy

Innovation

• vector quantization
• invariance entropy
• forward invariance
• Lipschitz-based reachable sets
• sum-of-squares programming