Matrix rank minimization approach to signal recovery and nonlinear function estimation for nonlinear ARX model with input nonlinearity

摘要

This paper deals with an input/output signal recovery problem for nonlinear multiple-input single-output autoregressive exogenous (ARX) models with input nonlinearity, which are used in data-driven systems biology. A matrix rank minimization approach is applied, and a new signal recovery algorithm for nonlinear ARX models is provided. The proposed algorithm recovers output signals and nonlinear-transformed input signals on a linear subspace using some assumptions about nonlinear functions and does not require the exact knowledge of nonlinear functions. Numerical examples using experimental data of signal transduction of cellular systems show the efficiency of the proposed algorithm.