A Two‐Stage Auxiliary Model Gradient Algorithm With for Parameter Estimation of Nonlinear Fractional‐Order Model

This article focuses on the identification of parameters for the fractional‐order nonlinear system driven by colored noise. An auxiliary model gradient descent (AM‐GD) algorithm is derived to address the identification problem of unknown inputs in the system. For the purpose of increasing the performance of the algorithm, we divide the system into two subsystems, a two‐stage auxiliary model gradient descent (2S‐AM‐GD) algorithm is derived by implementing the hierarchical identification principle, which decomposes the identification model into two subsystems. In comparison to the AM‐GD algorithm, the 2S‐AM‐GD algorithm shows a notable reduction in computational complexity. Finally, the proposed algorithm is evaluated through a series of simulation examples to assess its effectiveness.