A Case of Adaptive Nonlinear System Identification with Third Order Tensors in TensorFlow

Abstract

Non-linear system identification is a challenging problem with a plethora of engineering applications including digital telecommunications, adaptive control of biological systems, assessing integrity of mechanical constructs, and geological surveys. Various approaches have been proposed in the scientific literature, including Volterra and multivariate Taylor series, fuzzy neural networks, state space models, and wavelets. This conference paper proposes a succinct model of a non-linear system with memory based on a third order tensor whose coefficients are trained in an LMS-like way. Moreover, two variants deriving from sign LMS and batch LMS algorithms respectively are also implemented in TensorFlow. The results of applying the three training algorithms to this system are compared in terms of the mean square error in validation phase, the convergence rate of the coefficients, and the convergence rate of the Euclidean norm of the local gradients of the system model.