Polynomial Nonlinear Fractional State Space System Identification

This paper deals with the problem of identification of fractional Hammerstein systems. This model consists of a static nonlinear block in series with a linear fractional-order state space system. This problem poses different difficulties, because, it consists of estimating the system parameters, the states and the fractional order. To simplify this problem, we assume in this paper that the fractional order is known, then, a new identification algorithm is performed: firstly, the parameters of both the linear and the nonlinear subsystems are estimated based on the Least Squares algorithm, then, the states are updated based on the auxiliary model principle using the estimated parameters. Finally, a numerical simulation is realized in the extent to evaluate the performance of the presented method.

[1]  Yuewei Dai,et al.  A Modified Quantum Bacterial Foraging Algorithm for Parameters Identification of Fractional-Order System , 2018, IEEE Access.

[2]  Yuquan Chen,et al.  Identification for Hammerstein nonlinear ARMAX systems based on multi-innovation fractional order stochastic gradient , 2018, Signal Process..

[3]  K. Worden,et al.  Past, present and future of nonlinear system identification in structural dynamics , 2006 .

[4]  Dominik Sierociuk,et al.  Some applications of fractional order calculus , 2010 .

[5]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[6]  M. D. Narayanan,et al.  Parametric identification of fractional-order nonlinear systems , 2018 .

[7]  Weihua Deng,et al.  Remarks on fractional derivatives , 2007, Appl. Math. Comput..

[8]  Michael Pecht,et al.  A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors , 2018, Journal of Power Sources.

[9]  J. A. Tenreiro Machado,et al.  Fractional Calculus: Fundamentals and Applications , 2018 .

[10]  S. Ray.  Fractional Calculus with Applications for Nuclear Reactor Dynamics , 2015 .

[11]  Zhe Gao,et al.  System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay. , 2018, ISA transactions.

[12]  Yangquan Chen,et al.  Genetic Algorithm-Based Identification of Fractional-Order Systems , 2013, Entropy.

[13]  Rachid Mansouri,et al.  Vector Fitting fractional system identification using particle swarm optimization , 2008, Appl. Math. Comput..