Nonlinear system identification employing automatic differentiation

TL;DR

This paper introduces a novel nonlinear system identification method that uses automatic differentiation to accurately compute Jacobians, improving the efficiency and precision of state and parameter estimation, including for delay differential equations.

Contribution

The paper presents a new optimization-based estimation approach utilizing automatic differentiation for Jacobian computation, extending to delay differential equations.

Findings

Automatic differentiation provides exact derivatives without approximation errors.

The method improves estimation accuracy and convenience over numerical and symbolic differentiation.

Extension to delay differential equations enables estimation of delay parameters.

Abstract

An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost function and provides exact values of the derivatives. In contrast to numerical differentiation it is not suffering from approximation errors and compared to symbolic differentiation it is more convenient to use, because no closed analytic expressions are required. Furthermore, we demonstrate how to generalize the parameter estimation scheme to delay differential equations, where estimating the delay time requires attention.