Identification of system with distributed-order derivatives
-
Jun-Sheng Duan
and
Yu Li
Abstract
The identification problem for system with distributed-order derivative was considered. The order-weight distribution was approximated by piecewise linear functions. Then the discretized order-weight distribution was solved in frequency domain by using the least square technique based on the Moore-Penrose inverse matrix. Finally, five representative numerical examples were used to illustrate the validity of the method. The identification results are satisfactory, especially for the continuous order-weight distributions. In addition, the overlapped Bode magnitude frequency responses from the identified and exact transfer functions imply the effectiveness of the method.
Acknowledgements
The authors thank the National Natural Science Foundation of China for the support, under Grant No 11772203.
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Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books
- Survey Paper
- Towards a unified theory of fractional and nonlocal vector calculus
- Research Paper
- An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
- Analysis of solutions of some multi-term fractional Bessel equations
- Existence of solutions for the semilinear abstract Cauchy problem of fractional order
- Summability of formal solutions for a family of generalized moment integro-differential equations
- Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
- Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
- First order plus fractional diffusive delay modeling: Interconnected discrete systems
- On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
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- Output error MISO system identification using fractional models
- Short Paper
- Identification of system with distributed-order derivatives
- Short note
- On the Green function of the killed fractional Laplacian on the periodic domain
Articles in the same Issue
- Frontmatter
- Editorial
- FCAA related news, events and books
- Survey Paper
- Towards a unified theory of fractional and nonlocal vector calculus
- Research Paper
- An adaptive memory method for accurate and efficient computation of the Caputo fractional derivative
- Analysis of solutions of some multi-term fractional Bessel equations
- Existence of solutions for the semilinear abstract Cauchy problem of fractional order
- Summability of formal solutions for a family of generalized moment integro-differential equations
- Analysis and fast approximation of a steady-state spatially-dependent distributed-order space-fractional diffusion equation
- Green’s function for the fractional KdV equation on the periodic domain via Mittag–Leffler function
- First order plus fractional diffusive delay modeling: Interconnected discrete systems
- On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function
- On the decomposition of solutions: From fractional diffusion to fractional Laplacian
- Output error MISO system identification using fractional models
- Short Paper
- Identification of system with distributed-order derivatives
- Short note
- On the Green function of the killed fractional Laplacian on the periodic domain
