Fractional order system identification using a joint multi-innovation fractional gradient descent algorithm

This paper proposes a joint multi-innovation fractional gradient descent identification algorithm for fractional order systems. First, the flexibility of fractional calculus is leveraged to design a joint fractional gradient descent algorithm capable of estimating system parameters and unknown orders. The estimated system parameters are used as the initial conditions to identify the unknown order, and the identified order is used as the update conditions for the system parameters. Through the joint iteration of two fractional order gradients, both the identified order and parameters are updated. In addition, multi-innovation theory is applied to extend the joint fractional gradient descent algorithm to a joint multi-innovation fractional gradient descent algorithm, which improves the system identification accuracy. Then, the convergence of the algorithm is theoretically analyzed. Finally, the effectiveness of the algorithm is verified through numerical simulation and an experiment on the identification of an actual flexible linkage system.