Fractional gradient descent algorithms for systems with outliers: A matrix fractional derivative or a scalar fractional derivative

• Published in: Chaos, solitons and fractals Vol. 174; p. 113881
• Main Authors: Cao, Yuan, Su, Shuai
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2023
• Subjects: Computational efforts; Convergence rate; Fractional based method; Outliers; Parameter estimation; Outliers; Convergence rate; Parameter estimation; Fractional based method; Computational efforts
• ISSN: 0960-0779
• DOI: 10.1016/j.chaos.2023.113881

Two gradient descent based fractional methods are proposed for systems with outliers in this paper. The outliers in the collected data usually causes biased estimates, resulting in a poor identification model. Tradition fractional gradient descent (FGD) algorithm has an assumption that the fractional derivative is a scalar, which leads to slow convergence rates, especially for systems with an ill-conditioned matrix. The proposed algorithms in this paper have several advantages over the traditional identification methods: (1) can get unbiased estimates; (2) have faster convergence rates; (3) enrich the FGD estimation framework. Simulation examples demonstrate the effectiveness of the proposed algorithms. •Can get unbiased estimates.•Have faster convergence rates.•Enrich the FGD estimation framework.