Parameter Estimation of Two Classes of Nonlinear Systems with Non-separable Nonlinear Parameterizations

TL;DR

This paper introduces a globally convergent online estimator for nonlinear systems with non-separable exponential nonlinearities, applicable to practical fields like fuel cells and musculoskeletal dynamics, without restrictive assumptions.

Contribution

It presents a novel estimation method that guarantees parameter convergence under weak excitation, avoiding high-gain or complex computational techniques.

Findings

Estimator successfully applied to fuel cell systems

Estimator demonstrated in human musculoskeletal dynamics

Guarantees parameter convergence with weak excitation

Abstract

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical applications, and none of the existing parameter estimators is able to deal with them in an efficient way. The proposed estimation procedure is illustrated with two modern applications: fuel cells and human musculoskeletal dynamics. The procedure does not assume that the parameters live in known compact sets, that the nonlinearities satisfy some Lipschitzian properties, nor rely on injection of high-gain or the use of complex, computationally demanding methodologies. Instead, we propose to design a classical on-line estimator whose dynamics is described by an ordinary differential equation given in a compact precise form. A further contribution of the paper is the proof that parameter convergence is guaranteed with the extremely weak interval excitation requirement.