Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach

2025-08-18

AI Summary

To address the challenges of modeling and precise control in nonlinear dynamical systems, this paper proposes a data-driven feedback linearization framework. Methodologically, it integrates sparse regression with Lie derivative analysis to construct an output function dictionary and enforce relative-degree constraints; notably, it introduces Lie-derivative-based augmented constraints—first applied in system identification—to jointly discover the governing dynamics and eliminate internal dynamics. By deeply unifying geometric control theory with data-driven modeling, the framework eliminates reliance on prior system knowledge. Experiments demonstrate high-accuracy identification of control-affine equations for real physical systems and achieve exact feedback linearization, significantly improving control precision and robustness. Key contributions include: (i) a Lie-derivative-guided augmented constraint mechanism; (ii) an integrated design unifying system identification and feedback linearization; and (iii) synergistic use of stacked regression and relative-degree conditions.

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Abstract

Discovering the governing equations of a physical system and designing an effective feedback controller remains one of the most challenging and intensive areas of ongoing research. This task demands a deep understanding of the system behavior, including the nonlinear factors that influence its dynamics. In this article, we propose a novel methodology for identifying a feedback linearized physical system based on known prior dynamic behavior. Initially, the system is identified using a sparse regression algorithm, subsequently a feedback controller is designed for the discovered system by applying Lie derivatives to the dictionary of output functions to derive an augmented constraint which guarantees that no internal dynamics are observed. Unlike the prior related works, the novel aspect of this article combines the approach of stacked regression algorithm and relative degree conditions to discover and feedback linearize the true governing equations of a physical model.

Problem

• Identifying feedback linearized physical systems from prior dynamics
• Designing controllers using Lie derivatives and sparse regression
• Combining stacked regression with relative degree conditions

Innovation

• Lie derivatives for feedback linearization
• Stacked regression for system identification
• Augmented constraint to eliminate internal dynamics