Initialization of fractional order systems for the joint estimation of parameters and fractional differentiation orders

It has been recognized that the initialization of fractional-order systems requires time-varying functions. This factor is very intricate and affects the convergence properties of the parameters and fractional differentiation order estimation. For this reason, we propose a novel technique to simplify the pre-initialization process of fractional differential system by designing an appropriate initialization function that ensures the fast and precise convergence to the exact states of the systems. Subsequently, we present a joint estimation approach of the parameters and the fractional differentiation order for initialized fractional-order systems. The performance of the proposed method is illustrated through different numerical examples. Furthermore, a potential application of the algorithm is presented, which consists of joint estimation of parameters and fractional differentiation order of a fractional-order arterial Windkessel model.