Reservoir Predictive Path Integral Control for Unknown Nonlinear Dynamics

2025-09-03

AI Summary

To address the challenge of online modeling and control for unknown nonlinear dynamical systems, this paper proposes the Reservoir Predictive Path Integral (RPPI) framework. RPPI synergistically integrates the rapid dynamic modeling capability of Echo State Networks (ESNs) with the sampling-based stochastic optimal control mechanism of Model Predictive Path Integral (MPPI), augmented by an uncertainty-aware module that enables dynamic exploration-exploitation trade-offs. The framework supports parallelized nonlinear optimization, achieving both computational efficiency and robustness. Experimental evaluations on the Duffing oscillator and a quadruple-tank system demonstrate up to 60% reduction in control cost compared to conventional methods, along with显著 improvements in tracking accuracy and closed-loop stability. The core contributions include: (i) the first integration of ESNs with MPPI for real-time control, and (ii) a data-driven uncertainty quantification mechanism that enables adaptive, model-free online control—establishing a novel, efficient paradigm for controlling unknown nonlinear systems.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Neural networks capable of approximating complex nonlinearities have found extensive application in data-driven control of nonlinear dynamical systems. However, fast online identification and control of unknown dynamics remain central 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 -- to meet these challenges. The proposed reservoir predictive path integral (RPPI) enables fast learning of nonlinear dynamics with ESN and exploits the learned nonlinearities directly in parallelized MPPI control computation without linearization approximations. The framework is further extended to uncertainty-aware RPPI (URPPI), which leverages ESN uncertainty to balance exploration and exploitation: exploratory inputs dominate during early learning, while exploitative inputs prevail as model confidence grows. Experiments on controlling the Duffing oscillator and four-tank systems demonstrate that URPPI improves control performance, reducing control costs by up to 60% compared to traditional quadratic programming-based model predictive control methods.

Problem

• Fast online identification and control of unknown nonlinear dynamics
• Integrating echo-state networks with model predictive path integral control
• Balancing exploration and exploitation through uncertainty-aware control

Innovation

• Echo-state networks for fast nonlinear dynamics learning
• Parallelized MPPI control without linearization approximations
• Uncertainty-aware framework balancing exploration and exploitation