Identification of Complex Nonlinear Fractional-Order System Based on Fuzzy Multi-Model

Fractional-order dynamic systems, due to their long memory and nonlocality, have significant advantages in describing the dynamic behavior of complex engineering systems. However, existing identification methods often struggle to balance modeling accuracy and model structural complexity under conditions of strong nonlinearity, strong coupling, and multiple operating conditions. To address the challenge of modeling complex fractional-order systems with strong nonlinearity, strong coupling, and multiple operating conditions, this paper proposes a fuzzy multi-model modeling and identification method based on the decomposition-synthesis approach. First, a fractional-order fuzzy multi-model structure is constructed to characterize the dynamic characteristics of such complex systems. Second, an improved SKFCM hybrid clustering algorithm is proposed, combining K-means clustering and satisfactory fuzzy C-means clustering. This optimizes the cluster center selection strategy and overcomes the shortcomings of traditional satisfactory FCM algorithms, such as random initial membership and unreasonable cluster center selection, thus achieving a reasonable determination of the number of local models. Finally, the least-squares and Levenberg–Marquardt algorithms are integrated to interactively identify local model parameters, system fractional-order, and fuzzy scheduling function parameters, solving key difficulties such as unknown fractional-order s in antecedent variables, numerous parameter couplings, and difficulty in determining the antecedent space. Through academic examples and simulations of a robotic arm system, the proposed method effectively achieves high-precision modeling of complex fractional-order systems, demonstrating strong feasibility and superiority.