Adaptive Memory Identification of Fractional Order Systems - Zhao, Yang; Li, Yan; Zhou, Fengyu (Discontinuity, Nonlinearity, and Complexity, 2026)
This paper deals with a previously ignored problem that how to find the memory (initialization function) of fractional order system by using the recent sampled input-output data. A novel and practical strategy is proposed to estimate the initialization function, which adapts to all system parameters but fractional order. To implement this method, a P-type order learning approach is introduced to identify the system order separably and accurately, thanks to the fractional order sensitivity function. The initialization response is computed through an iterative learning identification strategy that guarantees the accuracy and adaptiveness simultaneously. Along with the estimations of order and initialization response, a practical piecewise identification criterion of initialization function is established by using the least squares and instrumental variable methods. The above strategy is available for both Caputo and Riemann-Liouville fractional order systems, where the initial values are applied rather than the initial conditions. Two illustrated examples are provided to support the conclusions.