Least squares and Instrumental Variable techniques for global identification of Fractional Differential Equation

In this work, a new estimation approach is proposed to improve the global convergence Output-Error (OE) identification method. The main disadvantage of the OE identification techniques is that they may converge to a secondary optimum. A good initialization converges to the global optimum. In this paper, Least squares (LS) method is selected as initialization step to OE algorithms. It´s extended to fractional system to identify unknown parameters and orders. However, the LS method may be too biased and may not lead to a good initialization. We present a new approach based on Instrumental variable (IV) to obtain a good initialization for OE methods. The results are encouraging and they have shown that the LS and IV method based on repeated fractional integration has to lead to a better initialization than arbitrary initialization. We investigate our identification theory with a Monte Carlo simulation that indicates the efficiency of the methods.