Online identification of non-homogeneous fractional order Hammerstein continuous systems based on the principle of multi-innovation

In the process of online identification of non-homogeneous fractional order Hammerstein systems in continuous time, traditional identification algorithms have slow convergence speed and low precision, and it is difficult to simultaneously identify multiple non-homogeneous fractional orders and system parameters. This paper proposes an identification method based on the principle of multi-innovation identification. Firstly, the Hammerstein non-homogeneous fractional order continuous-time system is given, and the parameters to be identified are clarified. Secondly, based on the Riemann–Liouville differential operator, the partial derivative equation of the objective function to non-homogeneous fractional orders in the identification process is given, which ensures that the coefficients of the system and non-homogeneous fractional orders can be identified at the same time. Then, within the given value range of the fractional vector, the partial derivative equation is progressively simplified to make it convenient for online calculation. And the principle of multi-innovation is introduced into the traditional Levenberg–Marquardt algorithm, which improves the convergence speed and convergence precision of the algorithm. Finally, we illustrate the validity of the theory through two experiments, including a numerical simulation example of a fractional-order system and a numerical example of a flexible manipulator system. Experiments prove that the algorithm proposed in this paper has good performance in both simulation examples and actual systems.