Adaptive Fractional-Order Gradient Dynamic Scheduling Strategy for Identifying Zero-Order T-S Models

This paper proposes a dynamic scheduled fractional-order gradient descent method (DSFGD) to enhance the training of zero-order Takagi-Sugeno (T-S) neuro-fuzzy models, which combine fuzzy reasoning and neural network architectures. By incorporating the Connection Cloud Model (CCM) as a fractional-order scheduler, our framework dynamically adjusts the derivative order during optimization. Transitioning from higher orders for rapid convergence in the early iterations to lower orders for precision refinement in later stages. The algorithm takes advantage of the complementary benefits of fractional calculus, such as non-local memory effects and a balanced search-utilization trade-off, while ensuring computational efficiency through optimized gradient calculations. A discussion of the convergence behavior is provided, supported by theoretical analysis and numerical validation. Extensive numerical experiments on function approximation and classification benchmarks show significant improvements: DSFGD outperforms integer-order methods in terms of lower test errors and achieves higher average classification accuracy, along with accelerated convergence rates across a range of model complexities. The proposed method also demonstrates robustness to hyperparameter variations, surpassing both fixed fractional-order and traditional gradient descent approaches. This work bridges the gap between fractional-order optimization and traditional modeling systems, offering a versatile framework for tackling complex nonlinear modeling tasks.