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

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.