Real-time capable nonlinear pantograph models using local model networks in state-space configuration

Hysteresis Identification using Nonlinear State-Space Models

Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinea...

Identification of nonlinear systems using Polynomial Nonlinear State Space models

Structured Inference Networks for Nonlinear State Space Models

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are m...

Time Series Prediction with Variational Bayesian Nonlinear State-Space Models

In this paper the variational Bayesian method for learning nonlinear state-space models introduced by Valpola and Karhunen in 2002 is applied to prediction in the ESTSP’07 time series prediction competition data set. The data set is pre-processed by approximately removing the periodic component of the data and the nonlinear state-space model is only learned on the residuals. The model uses mult...

Variational Bayes for Continuous-Time Nonlinear State-Space Models

We present an extension of the variational Bayesian nonlinear state-space model introduced by Valpola and Karhunen in 2002 [1] for continuous-time models. The model is based on using multilayer perceptron (MLP) networks to model the nonlinearities. Moving to continuous-time requires solving a stochastic differential equation (SDE) to evaluate the predictive distribution of the states, but other...