Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems

TL;DR

This paper introduces a computer-implemented algorithm for constructing homogeneous approximations of nonlinear control systems, utilizing algebraic and combinatorial methods, and demonstrates its application via a web-based tool.

Contribution

The paper develops a novel algorithm based on algebraic and combinatorial techniques for nonlinear control system approximation, implemented as an accessible web application.

Findings

Algorithm effectively constructs homogeneous approximations

Web application demonstrates practical usability

Method is suitable for computer implementation

Abstract

We present a 'calculator' for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and combinatorial tools, so, it is perfectly adapted to computer realization. We describe the algorithm and discuss its capabilities and limitations. We present its implementation as a web application and show by example how this app works.