Hierarchical fractional-order Hammerstein system identification

Abstract

For the fractional-order Hammerstein system with white noise, the difficulty of identification is that the parameters of the linear and the nonlinear blocks and the fractional order are unknown and the intermediate variable and the states are unmeasurable. To overcome this difficulty, we transform the system from an input nonlinear pseudo-state-space system to an input–output representation and we develop an algorithm based on the Recursive Least Squares, the Levenberg–Marquardt and the Auxiliary Model Principle. The convergence of the identified parameters is studied. The performance of the proposed algorithm are tested by two numerical examples.

Keywords:

• Fractional-order Hammerstein system
• identification
• state estimation
• Levenberg–Marquardt algorithm
• recursive least squares algorithm
• auxiliary model principle

Acknowledgments

This work was supported by Ministry of High Education and Scientific Research-Tunisia.

Disclosure statement

No potential conflict of interest was reported by the authors.