Damage Modeling for the Tree-Like Network with Fractional-Order Calculus

TL;DR

This paper introduces a fractional-order calculus-based model for damaged tree-like networks, enabling better understanding, control, and damage identification in such systems.

Contribution

It presents a novel fractional-order modeling approach for damaged networks, providing a structured disturbance model linked to damage levels, applicable beyond the specific case.

Findings

Modeling damaged networks as fractional-order systems clarifies their behavior.

The approach aids in designing robust controllers under damage uncertainty.

The structured disturbance model helps in damage identification.

Abstract

In this paper, we propose that a tree-like network with damage can be modeled as the product of a fractional-order nominal plant and a fractional-order multiplicative disturbance, which is well structured and completely characterized by the damage amount at each damaged component. Such way of modeling brings us insights about that damaged network's behavior, helps us design robust controllers under uncertain damages and identify the damage. Although the main result in this paper is specialized to one model, we believe that this way of constructing a well-structured disturbance model can be applied to a class of damaged networks.