Minimal Information Control Invariance via Vector Quantization
This addresses safety and computational efficiency for autonomous systems, though it appears incremental as it builds on existing invariance entropy and learning-based control frameworks.
The paper tackles the problem of designing safe, low-complexity controllers for autonomous systems by determining how few distinct control signals are needed to maintain state constraints, achieving a 157× reduction in codebook size on a 12D quadrotor model while preserving invariance.
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.