Neural networks have found extensive application in data-driven control of nonlinear dynamical systems, yet fast online identification and control of unknown dynamics remain central challenges. To meet these challenges, this paper integrates echo-state networks (ESNs)--reservoir computing models implemented with recurrent neural networks--and model predictive path integral (MPPI) control--sampling-based variants of model predictive control. The proposed reservoir predictive path integral (RPPI) enables fast learning of nonlinear dynamics with ESNs and exploits the learned nonlinearities directly in MPPI control computation without linearization approximations. This framework is further extended to uncertainty-aware RPPI (URPPI), which achieves robust stochastic control by treating ESN output weights as random variables and minimizing an expected cost over their distribution to account for identification errors. Experiments on controlling a Duffing oscillator and a four-tank system demonstrate that URPPI improves control performance, reducing control costs by up to 60% compared to traditional quadratic programming-based model predictive control methods.

翻译：神经网络在非线性动力学系统的数据驱动控制中已得到广泛应用，然而对未知动力学系统进行快速在线辨识与控制仍是核心挑战。为应对这些挑战，本文融合了回声状态网络（一种基于循环神经网络实现的储层计算模型）与模型预测路径积分控制（一种基于采样的模型预测控制变体）。所提出的储层预测路径积分控制方法能够利用回声状态网络快速学习非线性动力学，并将学习到的非线性特性直接用于模型预测路径积分控制计算，无需进行线性化近似。该框架进一步扩展为不确定性感知的储层预测路径积分控制方法，该方法通过将回声状态网络的输出权重视为随机变量，并最小化其分布上的期望成本以补偿辨识误差，从而实现了鲁棒的随机控制。通过对杜芬振子和四水箱系统的控制实验表明，相较于传统的基于二次规划的模型预测控制方法，不确定性感知的储层预测路径积分控制方法将控制性能提升了最高达60%的控制成本降低。