Accelerated Gradient Descent Algorithm for Systems With Missing Input Data Using Inverse Auxiliary Model

Abstract

This paper proposes two accelerated gradient descent algorithms for systems with missing input data with the aim at achieving fast convergence rates. Based on the inverse auxiliary model, the missing data can be obtained; and then by using the gradient descent method, the unknown parameters can be estimated. To improve the estimation efficiency of the gradient descent method, two accelerated techniques: fractional gradient descent algorithm and stage Aitken gradient descent algorithm, are introduced, which can increase the convergence rates and do not require computing the step-size. Compared with the traditional methods, the proposed methods can: 1) have faster convergence rates; 2) have no limitation on the input data; and 3) are robust to the step-size. The simulation examples show effectiveness of the proposed algorithms.

Keywords

• System identification
• fractional gradient descent algorithm
• Aitken method
• missing input data
• convergence rate