System-theoretic Analysis of Nonlinear Infinite-dimensional Systems with Generalized Symmetries

TL;DR

This paper extends symmetry-based observability analysis to a broader class of nonlinear infinite-dimensional systems by incorporating non-vertical and generalized symmetries, enhancing applicability.

Contribution

It introduces an extension of existing symmetry-based methods to include non-vertical and generalized symmetries for infinite-dimensional systems.

Findings

Broadened the class of systems analyzable with symmetry methods

Enhanced observability analysis capabilities for nonlinear systems

Applicable to systems lacking vertical classical symmetries

Abstract

Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution, we extend an existing approach, which is based on vertical classical symmetries, to non-vertical classical symmetries and generalized symmetries. This makes the approach applicable to a much larger class of systems, since many nonlinear systems do not possess any vertical classical symmetries.