Joint Estimation of Parameters and States of Fractional‐Order State‐Space Systems Based on Hierarchical Principle

ABSTRACT This study addresses the problem of identifying unknown parameters in fractional‐order state‐space (FOSS) systems, which more accurately capture the dynamic behavior of actual systems compared to their integer‐order counterparts. The parameter identification of the FOSS systems is an important research topic in control theory. As the dimension of the FOSS systems increases, the computational complexity of the identification algorithm also increases. In addition, the process of identifying unknown states further complicates the problem. We adopt a hierarchical identification method to achieve joint estimation of states and parameters. The interactive estimation of parameters and states is achieved by using the hierarchical multi‐innovation least squares algorithm for parameter estimation and the Kalman filtering for estimating unknown states. Finally, two simulation examples and an application example are employed to verify the effectiveness of the proposed algorithm. The simulation results show that this method has high identification accuracy and fast convergence speed for FOSS systems.