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

TL;DR

This paper introduces a new method combining stacked regression and Lie derivatives to identify and linearize nonlinear control systems, enabling more accurate feedback control design based on learned governing equations.

Contribution

It presents a novel approach that integrates stacked regression with Lie derivatives and relative degree conditions for system identification and feedback linearization.

Findings

Successfully identifies system dynamics using sparse regression.

Achieves feedback linearization ensuring no internal dynamics are observed.

Demonstrates improved accuracy over prior methods.

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.