Adaptive MPPI with Online Disturbance Covariance Estimation: Provable Stability Tightening via Spatial Smoothing

What the math gives to ML

The paper provides a constructive mechanism for adapting an unknown, state-dependent disturbance covariance while preserving a closed-loop stability certificate. Its key transferable asset is the separation of covariance-estimation error into a decreasing stochastic-approximation term, a fixed spatial-smoothing bias, and a temporal-drift term, together with a visitation-weighted diffusion kernel that is dissipative in the Lyapunov norm. The most promising neural-network transfer is an uncertainty-adaptive MPPI policy or world-model controller whose rollout sampling covariance is estimated online from observed transition residuals and spatially smoothed over latent-state cells. This yields a falsifiable crossover prediction: adaptation should outperform a fixed covariance after a computable sample count whenever the fixed covariance mismatch exceeds the smoothing-bias-plus-drift allowance.