適応MPPIとオンライン外乱共分散推定：空間平滑化による証明可能な安定性の強化
Adaptive MPPI with Online Disturbance Covariance Estimation: Provable Stability Tightening via Spatial Smoothing
未知で空間的に変動する外乱共分散を持つ非線形システムに対し、オンライン推定と空間拡散を組み合わせた適応MPPI制御を提案し、安定性証明の改善を示した論文。
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著者: Hyung-Jin Yoon, Hunmin Kim
分類: eess.SY, cs.RO, cs.SY, math.OC
原文アブストラクト
We study Model Predictive Path Integral (MPPI) control for nonlinear systems with additive process disturbances whose covariance is unknown, spatially varying, and slowly time-varying. A mismatched disturbance covariance produces a persistent penalty in closed-loop stability certificates, while online estimation can reduce this penalty as data are collected. We propose a cell-wise recursive covariance estimator with spatial diffusion and prove a finite-horizon error bound that separates stochastic-approximation error, spatial-smoothing bias, and temporal-drift effects. The diffusion kernel is chosen to be reversible with respect to the stationary visitation measure, making the diffusion operator dissipative in the weighted Lyapunov analysis. We then substitute the resulting covariance estimate into the MPPI sampling distribution and derive an adaptive stability certificate with an explicit learning penalty. The main result is a payoff theorem: after a computable crossover time, the adaptive controller achieves a strictly tighter certified stability bound than any fixed covariance choice whose mismatch exceeds the residual smoothing and drift allowance. Numerical experiments illustrate the estimator convergence and the resulting stability-tightening effect.
