Parameter identification of fractional order system using enhanced response sensitivity approach

This paper presents an investigation on parameters identification of fractional order system based on the enhanced response sensitivity approach. Compared with the integer order differential operator, fractional order operator can describe the characteristics of some phenomena more accurately such as hereditary and memory properties. In order to achieve the solution of the fractional order system, a new computational scheme is presented in this paper based on Adams-type scheme and the Newmark -β method. Such an identification problem is classed as an inverse problem and can be modeled as an nonlinear optimization problem. In this paper, the enhanced response sensitivity approach is derived and used to identify the parameters of the fractional order system. To this end, the time domain response of the fractional order system is obtained by the proposed computational scheme, then the response sensitivity with respect to the parameter is achieved as well. Numerical examples illustrated the computing and identification procedure and shown the accuracy and the convergence of identification scheme.