Minimal Information Control Invariance via Vector Quantization

• URL: http://arxiv.org/abs/2604.03132v1
• Date: Fri, 03 Apr 2026 15:53:07 GMT
• Title: Minimal Information Control Invariance via Vector Quantization
• Abstract summary: We study how many distinct control signals are needed to render a compact set forward invariant under sampled-data control.<n>We propose a vector-quantized autoencoder that jointly learns a state-space partition and a finite control codebook.<n>We empirically characterize the minimum sensing resolution compatible with safe operation.
• Score: 2.094349987888854
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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