Data-Driven Nonlinear Regulation: Gaussian Process Learning

2025-06-10

AI Summary

This paper addresses the output regulation problem for nonlinear systems subject to modeling errors and model uncertainties. We propose a fully data-driven Gaussian process (GP) regression-based output feedback controller that obviates conventional model-dependent observers by directly learning the unknown internal model’s steady-state mapping online, thereby integrating nonlinear control design with data-driven modeling. Rigorous analysis establishes uniform ultimate boundedness of the closed-loop system states; moreover, the radius of the ultimate bound monotonically decreases with increasing GP approximation accuracy. Numerical experiments demonstrate strong robustness against both parametric uncertainties and modeling inaccuracies. The key contribution lies in the first-ever model-free, online learning of the internal model—eliminating the need for prior structural knowledge—thereby significantly enhancing the practical applicability and reliability of output regulation frameworks for real-world nonlinear systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This article addresses the output regulation problem for a class of nonlinear systems using a data-driven approach. An output feedback controller is proposed that integrates a traditional control component with a data-driven learning algorithm based on Gaussian Process (GP) regression to learn the nonlinear internal model. Specifically, a data-driven technique is employed to directly approximate the unknown internal model steady-state map from observed input-output data online. Our method does not rely on model-based observers utilized in previous studies, making it robust and suitable for systems with modelling errors and model uncertainties. Finally, we demonstrate through numerical examples and detailed stability analysis that, under suitable conditions, the closed-loop system remains bounded and converges to a compact set, with the size of this set decreasing as the accuracy of the data-driven model improves over time.

Problem

• Solves output regulation for nonlinear systems using data-driven approach
• Uses Gaussian Process regression to learn nonlinear internal model online
• Ensures closed-loop stability under modeling errors and uncertainties

Innovation

• Gaussian Process regression for nonlinear learning
• Data-driven online approximation of steady-state map
• Robust output feedback without model-based observers