Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems

Abstract

• Fractional adaptive algorithms are designed for parameter estimation of CARAR systems. • Algorithms remain convergent for all noise and fractional order variations. • Accuracy of proposed fractional strategies is better than for standard methods. • Proposed algorithms can be exploited to solve complex and stiff control problems. • Proposed normalized fractional algorithms have comparable computational requirements. In this paper, strength of fractional adaptive signal processing is exploited for parameter identification of control autoregressive autoregressive (CARAR) systems using normalized version of fractional least mean square (FLMS) and its recently introduced modification of type 1 and 2. The adaptation performance of the proposed normalized FLMS methods is compared with standard counterparts for CARAR identification model by taking different noise levels as well as fractional orders. The results of the statistical analyses are used to validate the consistency of the proposed normalized fractional adaptive methodologies in terms of convergence, accuracy and robustness. The reliability and effectiveness of the design schemes is further validated through consistently approaching the desired identification parameters based on performance metrics of mean square error, variance account for and Nash–Sutcliffe efficiency.