TY - JOUR
T1 - Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems
AU - Belkhatir, Zehor
AU - Laleg-Kirati, Taous Meriem
N1 - Funding Information:
Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST) . The authors are thankful to the anonymous reviewers and the associate editor for their valuable comments that helped to improve the quality of the paper.
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/5
Y1 - 2018/5
N2 - This paper proposes a two steps algorithm for the joint estimation of parameters and fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. A potential application of the proposed algorithm consists in estimating the fractional differentiation orders of a fractional neurovascular model along with the neural activity considered as an input for this model. To assess the performance of the proposed method, different numerical tests are conducted.
AB - This paper proposes a two steps algorithm for the joint estimation of parameters and fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. A potential application of the proposed algorithm consists in estimating the fractional differentiation orders of a fractional neurovascular model along with the neural activity considered as an input for this model. To assess the performance of the proposed method, different numerical tests are conducted.
KW - Linear fractional order systems
KW - Modulating functions method
KW - Non-commensurate orders
KW - Parameters and fractional differentiation orders estimation
UR - http://www.scopus.com/inward/record.url?scp=85044121348&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2018.02.012
DO - 10.1016/j.sysconle.2018.02.012
M3 - Article
AN - SCOPUS:85044121348
SN - 0167-6911
VL - 115
SP - 26
EP - 33
JO - Systems and Control Letters
JF - Systems and Control Letters
ER -