Data-driven Nonlinear System Identification Under Bounded Noise Using Kernel Learning-based Ellipsoidal Set-membership

Abstract

Nonlinear system identification under bounded interferences remains a challenging problem when the noise bound is unavailable a priori. This paper presents a recursive kernel-based set-membership identification algorithm that combines the ellipsoidal outer-bounding (EOB) set-membership method with kernel learning to address this issue. Instead of identifying the nonlinear system directly in the input space, the proposed method exploits a reproducing kernel Hilbert space (RKHS), where the nonlinear estimation problem is represented as a linear regression model. Furthermore, a recursive data-driven procedure is introduced to estimate the noise bound simultaneously with the model parameters. Theoretical convergence properties of the proposed algorithm are determined. The performance of the proposed algorithm is validated through numerical simulation.