Data-Driven Newton Raphson Controller Based on Koopman Operator Theory

TL;DR

This paper introduces a data-driven Newton-Raphson control method using Koopman operator theory to model nonlinear systems from data, enabling practical and effective control without explicit system models.

Contribution

It proposes a novel approach combining Koopman operator theory with Newton-Raphson control, avoiding the need for explicit system models or derivatives.

Findings

Effective control of highly nonlinear systems demonstrated

Data-driven approach reduces reliance on explicit models

Method applicable with collected data only

Abstract

Newton-Raphson controller is a powerful prediction-based variable gain integral controller. Basically, the classical model-based Newton-Raphson controller requires two elements: the prediction of the system output and the derivative of the predicted output with respect to the control input. In real applications, the model may not be known and it is infeasible to predict the system sometime ahead and calculate the derivative by finite difference method as done in simulation. To solve these problems, in this work, we utilize the Koopman operator framework to reconstruct a linear model of the original nonlinear dynamical system and then utilize the output of the new linear system as the predictor of the Newton-Raphson controller. This method is only based on collected data within some time instant thus more practical. Three examples related to highly nonlinear systems are provided to verify the effectiveness of our proposed method.