Data-driven Identification of Approximate Passive Linear Models for Nonlinear Systems

S Sivaranjani, Etika Agarwal, Vijay Gupta

Abstract: In model-based approaches to learning for controller design, it is important to first identify a system model from input-output data. Assume that we have access to some information about the true system satisfying a structural property that makes it easy to design a controller and obtain a desired performance or stability guarantee on the closed loop system. Can we identify a system model that satisfies this property? In this paper, we consider the property to be that of passivity, that can be used to ensure stability with a learned controller. We present an algorithm to learn a passive linear model of a unknown passive nonlinear system from time domain input-output data. We first learn an approximate linear model of the nonlinear system using standard regression techniques. We then perturb the system matrices of the linear model to enforce passivity. We show that the perturbation can be chosen to ensure that the linear model closely approximates the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the passivity of the linear model guarantees local passivity of the unknown nonlinear system.