具有在线干扰协方差估计的自适应MPPI：通过空间平滑实现可证明的稳定收紧
Adaptive MPPI with Online Disturbance Covariance Estimation: Provable Stability Tightening via Spatial Smoothing
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中文总结 AI 辅助
研究具有未知、空间变化且时变干扰协方差的非线性系统的MPPI控制，提出带空间扩散的协方差估计器，证明有限时域误差界，代入MPPI采样分布得自适应稳定证书，结果表明自适应控制器能实现更紧稳定界，数值实验验证效果。
中文摘要 AI 辅助
我们研究了具有加性过程干扰的非线性系统的模型预测路径积分（MPPI）控制，其协方差未知、空间变化且时间缓慢变化。不匹配的干扰协方差会在闭环稳定证书中产生持续惩罚，而在线估计可以随着数据收集减少此惩罚。我们提出了一种具有空间扩散的逐单元递归协方差估计器，并证明了一个有限时域误差界，该界分离了随机逼近误差、空间平滑偏差和时间漂移效应。扩散核相对于平稳访问测度是可逆的，使得扩散算子在加权李雅普诺夫分析中是耗散的。然后，我们将得到的协方差估计代入MPPI采样分布，并推导出具有显式学习惩罚的自适应稳定证书。主要结果是一个收益定理：在一个可计算的交叉时间之后，自适应控制器实现了比任何不匹配超过剩余平滑和漂移允许量的固定协方差选择更严格的认证稳定界。数值实验说明了估计器的收敛性和由此产生的稳定收紧效果。
英文摘要
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.
发表机构
- Department of Mechanical and Nuclear Engineering, Tennessee Technological University（机械与核工程系，田纳西技术大学）
- School of Engineering, Department of Electrical and Computer Engineering, Mercer University（工程学院，电气与计算机工程系，梅尔基大学）
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