Deep State Space Models for Nonlinear System Identification

System identification of nonlinear state-space models

This paper is concerned with the parameter estimation of a general class of nonlinear dynamic systems in state-space form. More specifically, a Maximum Likelihood (ML) framework is employed and an Expectation Maximisation (EM) algorithm is derived to compute these ML estimates. The Expectation (E) step involves solving a nonlinear state estimation problem, where the smoothed estimates of the st...

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

Identification of the Silverbox Benchmark Using Nonlinear State-Space Models

This work presents the application of an initialization scheme for nonlinear statespace models on a real data benchmark example: the Silverbox problem. The goal of the proposed approach is to transform the identification of a nonlinear dynamic system into an approximate static problem, so that system dynamics and nonlinear terms are identified separately. Classic identification techniques are u...

Recursive Prediction Error Identification of Nonlinear State Space Models

A recursive prediction error algorithm for identification of systems described by nonlinear ordinary differential equation (ODE) models is presented. The model is a MIMO ODE model, parameterized with coefficients of a multi-variable polynomial that describes one component of the right hand side function of the ODE. It is explained why such a parameterization is a key to obtain a well defined al...