Control Performance Assessment with Fractional Lower Order Moments

Non-Gaussian statistical signal processing is be-coming increasingly significant in the current complex world. However, the variance of a non-Gaussian distribution may not exist, therefore many conventional methods will be considerably weakened, meaningless or even misleading. For example, the least-squares criterion may not be robust in the non-Gaussian environment, owing to the impulsive behaviors and outliers. In the paper, the statistical measures with fractional lower order moments (FLOM) are used instead of second-order moments to assess the control performance for non-Gaussian processes. The results show that FLOM is robust against outliers for the non-Gaussian signals. In the end, Hurst exponent fitting with FLOM and multifractal detrended fluctuation analysis (MFDFA) with FLOM are applied to the real data.