Time-varying Nonlinear Discrete-time Systems Identification Based on the Convex Combination of Two Multi-dimensional Taylor Networks*

The convex combination of two multi-dimensional Taylor networks (MTNs) is presented to identify the time-varying nonlinear discrete-time systems. By taking the weight coefficients of the two MTNs as time-varying parameters that need training online to reflect the system’s input and output changes. An improved recursive least squares (IRLS) algorithm that obtained by introducing a variable forgetting factor is used to train the weight coefficients for the first MTN, and the second MTN is trained by a normalized least squares algorithm. In addition, the sigmoid activation function and gradient algorithm are introduced to adjust the combination coefficient. The validity of the proposed method is confirmed through a numerical example.