Continuous-time Predictor-Based Subspace Identification with Hermite basis expansions

TL;DR

This paper introduces the Hermite-Domain PBSID method for continuous-time subspace identification of LTI systems, leveraging Hermite basis functions to directly estimate continuous-time state-space models.

Contribution

It proposes a novel Hermite-based approach that avoids time-shifts and directly identifies continuous-time system matrices, improving accuracy over existing methods.

Findings

The HD-PBSID method accurately estimates continuous-time system matrices.

It outperforms Laguerre-projection based CT-PBSID in simulation accuracy.

The method effectively avoids time-shifts by proper signal scaling.

Abstract

In this paper the problem of continuous-time subspace identification for Linear Time Invariant (LTI) systems is considered and a method which directly identifies a continuous-time state-space form is proposed. First, Hermite basis functions are used to project signals and obtain a finite number of Hermite coefficients. By exploiting recursive relations and time derivative properties of the Hermite basis functions, an expression of the derivative operator is obtained. The latter is then recursively applied, ensuring that the state-space matrices remain in continuous-time form and making the system suitable for the implementation of steps which are akin to those of the Predictor-Based Subspace IDentification (PBSID) method. This new method, hereby called the Hermite-Domain PBSID (HD-PBSID) method, has the further advantage of avoiding time-shifts by properly scaling the input and output signals. The performance of the proposed approach is illustrated in a simulation study aimed at showing the accuracy of the estimates and at comparing the HD-PBSID method and the Laguerre-projections based Continuous-Time PBSID (CT-PBSID) algorithm.