Kernel-based methods for Volterra series identification

Volterra series approximate a broad range of nonlinear systems. Their identification is challenging due to the curse dimensionality: number model parameters grows exponentially with complexity input–output response. This fact limits applicability such models and has stimulated recently much research on regularized solutions. Along this line, we propose two new strategies that use kernel-based methods. First, introduce multiplicative polynomial kernel (MPK). Compared standard kernel, MPK equipped richer set hyperparameters, increasing flexibility in selecting monomials really influence system output. Second, smooth decaying (SED-MPK), version which requires less allowing handle also high-order series. Numerical results show effectiveness approaches.