FO_Chaotic_SRSA

This repository contains codes and data for the following publication:

• Tao Zhang, Zhong-rong Lu, Ji-ke Liu, Guang, Liu*. [Parameter Estimation of Fractional Chaotic Systems Based on Stepwise Integration and Response Sensitivity Analysis]

SRSA is a parameter estimation approach for fractional chaotic systems based on stepwise integration and response sensitivity analysis.

Framework

FO_Chaotic_SRSA This program corresponds to the several numerical examples of this article

Repository Overview

forward problem

• data_unified.m - Codes for obtaining the measured data of fractional order unified system.
• data_Commensurate_PMSM.m - Codes for obtaining the measured data of commensurate fractional order PMSM system.
• data_Incommensurate_PMSM.m - Codes for obtaining the measured data of incommensurate fractional order PMSM system.

main program

• main_unified_SRSA.m - Codes for the parameter identification of fractional order unified system.
• main_Commensurate_PMSM_SRSA.m - Codes for the parameter identification of commensurate fractional order PMSM system.
• main_Incommensurate_PMSM_SRSA.m - Codes for the parameter identification of incommensurate fractional order PMSM system.

SRSA package

• FO_unified.m - Codes for the numerical response of fractional order unified system.
• FO_Commensurate_PMSM.m - Codes for the numerical response of commensurate fractional order PMSM system.
• FO_Incommensurate_PMSM.m - Codes for the numerical response of incommensurate fractional order PMSM system.
• FO_unified_SRSA.m - Codes for the Stepwise response and sensitivity of fractional order unified system.
• FO_Commensurate_PMSM_SRSA.m - Codes for the Stepwise response and sensitivity of commensurate fractional order PMSM system.
• FO_Incommensurate_PMSM_SRSA.m - Codes for the Stepwise response and sensitivity of incommensurate fractional order PMSM system.
• rzz.m - Codes for the binomial coefficients calculation.
• settick.m - Codes for figures.
• csvd.m l_corner.m l_curve.m lcfun.m polt_lc.m tikhonov.m - Codes form the Regularization Tools by Per Christian Hansen and IMM.

Citation

Please cite the following paper if you find the work relevant and useful in your research: Zhang, T., Lu, Zr., Liu, Jk. et al. Parameter estimation of fractional chaotic systems based on stepwise integration and response sensitivity analysis. Nonlinear Dyn (2023). https://doi.org/10.1007/s11071-023-08623-3