KLMS algorithm in Vector-Valued RKHS for online nonlinear MIMO systems identification.

This paper proposes an extension of the KLMS algorithm to the Vector-Valued Reproducing Kernel Hilbert Space (VV-RKHS), enabling the use of the operator-valued kernel (OV-kernel) in the online identification of multi-input multi-output (MIMO) nonlinear systems. The yielded multivariate kernel model offers more design flexibility and involves fewer parameters than other vector-valued KLMS algorithms present in the literature. Conditions ensuring the convergence of the proposed OV-KLMS algorithm are given. Experiments on a multivariate chaotic attractor as well as numerical simulations are carried out and show the effectiveness of the proposed algorithm.