Continuous-time Predictor-Based Subspace Identification with Hermite basis expansions
For control engineers and system identification researchers, this provides a new continuous-time identification method with potential advantages over existing approaches, though it is an incremental improvement.
The paper proposes a continuous-time subspace identification method (HD-PBSID) using Hermite basis expansions to directly identify state-space models for LTI systems, avoiding time-shifts. Simulation results show improved accuracy compared to the Laguerre-based CT-PBSID method.
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.