Interaction Identification of a Heterogeneous NDS with Quadratic-Bilinear Subsystems

TL;DR

This paper develops a method for identifying interaction parameters in heterogeneous networked dynamic systems with quadratic-bilinear subsystems, using time-domain data and explicit formulas without sampling restrictions.

Contribution

It introduces explicit formulas for transient and steady-state responses and an estimation algorithm for parameters and transfer functions in QBTI systems.

Findings

Explicit formulas for system responses are derived.

An estimation algorithm for parameters and transfer functions is proposed.

Numerical example demonstrates the effectiveness of the method.

Abstract

This paper attacks time-domain identification for interaction parameters of a heterogeneous networked dynamic system (NDS), with each of its subsystems being described by a continuous-time descriptor quadratic-bilinear time-invariant (QBTI) model. The obtained results can also be applied to parameter estimations for a lumped QBTI system. No restrictions are put on the sampling rate. Explicit formulas are derived respectively for the transient and steady-state responses of the NDS, provided that the probing signal is generated by a linear time invariant (LTI) system. Some relations have been derived between the NDS steady-state response and its frequency domain input-output mappings. These relations reveal that the value of some NDS associated generalized TFMs can in principle be estimated at almost any interested point of the imaginary axis from time-domain input-output experimental data, as well as its derivatives and a right tangential interpolation along an arbitrary direction. Based on these relations, an estimation algorithm is suggested respectively for the parameters of the NDS and the values of these generalized TFMs. A numerical example is included to illustrate characteristics of the suggested estimation algorithms.