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.