Data-Driven Strictly Positive Real System Identification with prior System Knowledge

TL;DR

This paper introduces a data-driven method for identifying strictly positive real (SPR) systems using prior system knowledge and GOBFs, ensuring the estimated transfer functions are physically meaningful and SPR.

Contribution

It presents a novel algorithm combining prior pole location estimates with convex optimization to accurately approximate SPR transfer functions from frequency response data.

Findings

Effective approximation of SPR transfer functions using GOBFs

Utilizes prior knowledge to improve system identification accuracy

Ensures estimated systems adhere to physical and stability constraints

Abstract

Strictly Positive Real (SPR) transfer functions arise in many areas of engineering like passivity theory in circuit analysis and adaptive control to name a few. In many physical systems, it is possible to conclude that the system is Positive Real (PR) or SPR but system identification algorithms might produce estimates which are not SPR. In this paper, an algorithm to approximate frequency response data with SPR transfer functions using Generalized Orthonormal Basis Functions (GOBFs) is presented. Prior knowledge of the system helps us to get approximate pole locations, which can then be used to construct GOBFs. Next, a convex optimization problem will be formulated to obtain an estimate of the SPR transfer function.