Reinforcement Learning-Based Output Feedback LQR for Continuous-Time MIMO Systems

What the math gives to ML

The paper provides a concrete identifiability mechanism for model-free output-feedback control: a dynamic input-output filter can produce a lifted vector with many deterministic redundant directions, even though only 2n components in SIMO systems and n(m+1) components in general MIMO systems are independent. This redundancy makes Bellman regressions rank deficient and causes unstable policy or value iteration. A strong transfer is to insert an online, rank-adaptive linear memory bottleneck before recurrent actor-critic or neural state-space models, using filtered histories rather than an unnecessarily large recurrent state. The key falsifiable prediction is that truncating the filter lift at its intrinsic numerical rank will remove near-zero singular values, improve regression conditioning, and create a sharp stability improvement near the rank threshold.