Hybrid Identification with Multi-Innovation Method Based on Fractional-Order Nonlinear State-Space Model

For Hammerstein system with fractional linear state space model, it is very difficult to build its model by identification method. The difficulty lies in that the nonlinear state space equation model describing the system contains unknown model parameters, fractional order of the system and outside noise. In order to overcome these difficulties, we transform the fractional system from an input nonlinear pseudo-state space model to an input-output regression model, and estimate the model parameters with multi-innovation recursive gradient descent algorithm, and confirm the fractional order with the multi-innovation Levenberg-Marquardt algorithm. Finally, the effectiveness of the algorithm is verified by a numerical example.