Parameter estimation of two classes of nonlinear systems with non-separable nonlinear parameterizations

Abstract

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing an exponential function whose power depends on unknown parameters. This class of non-separable nonlinearities appears in many practical applications, and none of the existing parameter estimators is able to deal with them in an efficient way. Our main technical contribution is the development of a lifting procedure for non-separable nonlinearly parameterized regressor equations to obtain separable ones, to which we can apply a recently reported estimation procedure. This is illustrated with a human musculoskeletal dynamics problem. The procedure does not assume that the parameters leave 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.

This paper is supported by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019-0898. This work is part of the project MAFALDA (PID2021-126001OBC31) and MASHED (TED2021-129927B-I00) funded by MCIN/ AEI/10.13039/501100011033 and by the European Union Next GenerationEU/PRTR

Peer Reviewed

Postprint (author's final draft)