# Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamics

arXiv: https://arxiv.org/abs/2509.03839 · HTML: https://mlsanity.com/paper/2509.03839/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 54 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Model Predictive Path Integral Control using Covariance Variable Importance Sampling](https://mlsanity.com/paper/1509.01149/) (2015)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks](https://mlsanity.com/paper/2103.02383/) (2021)
- [Risk-Aware Model Predictive Path Integral Control Using Conditional Value-at-Risk](https://mlsanity.com/paper/2209.12842/) (2022)
- [Recent Advances in Path Integral Control for Trajectory Optimization: An Overview in Theoretical and Algorithmic Perspectives](https://mlsanity.com/paper/2309.12566/) (2023)
- [Fast Explicit Machine Learning-Based Model Predictive Control of Nonlinear Processes Using Input Convex Neural Networks](https://mlsanity.com/paper/2408.06580/) (2024)
- [Gaussian Process Model Predictive Control of Unknown Nonlinear Systems](https://mlsanity.com/paper/1612.01211/) (2016)

## Built on by (most cited first, 1 of 1)

- [LoRA-RC: Reservoir Computing with Low-Rank Adaptation](https://mlsanity.com/paper/2609.12327/) (2026)

## Abstract (arXiv)

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.