Abstract
This paper presents a method for data-driven identification of passive systems, with a focus on systems with nonlinear friction models. This is achieved by approximating the passive dynamics of a given system in a reproducing kernel Hilbert space (RKHS). The main novelty of this approach is the use of a quadratic kernel model to ensure that the estimated friction dynamics is passive. The regularized regression is done by optimizing a convex Fenchel dual of the optimization problem. The method was validated with a simulation study, where it was first applied to the estimation of a Karnopp friction model with Stribeck effects. It was also applied to the identification of systems dynamics of a mass-spring-damper (MSD) system with the same friction model. The identification was performed using two different forms of input data: sampled input and output signals and the Legendre coefficients corresponding to these signals. Results demonstrated accurate identification of training data, as well as examples of generalization to test data. Passivity and causality of the approximated continuous system do not guarantee passivity and causality of its corresponding discretized or spectrally approximated system. Although simulation results demonstrate this, increasing the sample size could increase representation accuracy and thereby the preservation of these properties.