Inversion mechanism of uncertain orders and parameters for the non-commensurate and hyper fractional order chaotic systems via differential evolution

TL;DR

This paper introduces a differential evolution-based inversion mechanism for estimating uncertain fractional orders and parameters in non-commensurate and hyper fractional chaotic systems, demonstrating high accuracy and robustness.

Contribution

It proposes a novel inversion method using differential evolution algorithms for fractional chaotic systems, addressing the estimation of uncertain orders and parameters.

Findings

Successful estimation of fractional orders and parameters in chaotic systems

Method shows high precision in simulations

Robustness against uncertainties in system parameters

Abstract

In this paper, a novel uncertain fractional-orders and parameters' inversion mechanism via the differential evolution algorithms (DE) with a general mathematical model is proposed for non-commensurate and hyper fractional chaotic systems. The problems of fractional-order chaos' inversion estimation are converted into multiple modal non-negative objective functions' minimization, which takes fractional-orders and parameters as its particular independent variables. And the objective is to find optimal combinations of fractional-orders and systematic parameters by DE in the predefined intervals for fractional order chaotic systems such that the objective function is minimized. Simulations are done to estimate a series of non-commensurate and hyper fractional chaotic systems. The experiments' results show that the proposed inversion mechanism for fractional-order chaotic systems is a successful methods with the advantages of high precision and robustness.