Minimal Information Control Invariance via Vector Quantization

TL;DR

This paper introduces a vector-quantized autoencoder approach to minimize control information needed for safety invariance in autonomous systems, demonstrating significant codebook size reduction while maintaining safety.

Contribution

It presents a novel vector-quantized autoencoder method for control invariance, linking information theory with control, and develops an iterative certification algorithm for safety assurance.

Findings

Achieved 157x reduction in control codebook size on a quadrotor model.

Preserved safety invariance with reduced control complexity.

Characterized minimum sensing resolution 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.