1 results about "Fractional differential" patented technology

A parameter identification method for fractional-order time-delay systems based on the Gegenbauer wavelet operation matrix is ​​presented, addressing the problem that existing parameter identification methods cannot identify fractional-order systems with time delays. This method constructs a Gegenbauer wavelet operation matrix for both fractional-order integral operators and time-delay operators. Then, the original fractional-order time-delay differential equation is transformed into a system of algebraic equations, thus avoiding direct numerical approximation of fractional-order differential terms. Furthermore, a nonlinear least squares method is used to jointly estimate the fractional-order order, time-delay parameters, and system parameters. Finally, the optimal fractional-order order and model parameters are determined based on minimizing the error between the model output and the actual output. This method effectively reduces solution complexity and improves the numerical stability and accuracy of parameter identification. It provides an effective tool for high-precision modeling and analysis of fractional-order time-delay systems.