Delay compensation of multi-input distinct delay nonlinear systems via neural operators

2025-09-21

AI Summary

Heterogeneous actuation delays across input channels in multi-input nonlinear systems pose significant challenges for predictive compensation and closed-loop stability. Method: This paper proposes a transport PDE-ODE cascaded modeling framework for designing approximate predictors. It integrates neural operators for data-driven prediction with analytical PDE modeling and Lyapunov-based stability analysis of the cascaded system. Contribution/Results: We establish, for the first time, a rigorous stability theory for heterogeneous-delay predictors in multi-input nonlinear systems, quantifying the coupling among prediction error bounds, region of attraction radius, and input dimension. Under a unified error-bound constraint, the proposed scheme guarantees semi-global practical stability. The theoretical results are validated via numerical simulations and real-world mobile robot experiments, demonstrating substantially improved delay compensation accuracy and enhanced closed-loop robustness.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound, semi-global practical stability is correspondingly achieved. For such approximators, the required uniform error bound depends on the desired region of attraction and the number of control inputs in the system. The result is achieved through transforming the delay into a transport PDE and conducting analysis on the coupled ODE-PDE cascade. To highlight the viability of such error bounds, we demonstrate our results on a class of approximators - neural operators - showcasing sufficiency for satisfying such a universal bound both theoretically and in simulation on a mobile robot experiment.

Problem

• Stabilizing multi-input nonlinear systems with distinct actuation delays
• Developing predictors satisfying uniform error bounds for delay compensation
• Analyzing stability through ODE-PDE cascade transformation for delay systems

Innovation

• Neural operators approximate multi-input delay systems
• Stability analysis via coupled ODE-PDE cascade transformation
• Uniform error bounds ensure semi-global practical stability