Analysis of state space system identification methods based on instrumental variables and subspace fitting (original) (raw)
Related papers
A Subspace Based Instrumental Variable Method For State-Space System Identification
1994
Traditional prediction-error techniques for multivariable system identi cation require canonical descriptions using a large number of parameters. This problem may b e avoided using subspace based methods, since these estimate a state-space model directly from the data. In this paper, a subspace based technique for identifying general nite-dimensional linear systems is presented and analyzed. Similar to subspace based identi cation schemes, the space spanned by the extended observability matrix is rst estimated. The system parameters are then extracted by reparametrizing the nullspace of the subspace estimate in terms of the coe cients of the characteristic polynomial. A quadratic problem is obtain and based on a statistical analysis, an optimal weighting derived.
Performance of subspace based state-space system identification methods
1993
Traditional prediction-error techniques for multivariable system identi cation require canonical descriptions using a large number of parameters. This problem can be avoided using subspace based methods, since these estimate a state-space model directly from the data. The main computations consist of a QR-decomposition and a singular-value decomposition. Herein, a subspace based technique for identifying general nite-dimensional linear systems is presented and analyzed. The technique applies to general noise covariance structures. Explicit formulas for the asymptotic pole estimation error variances are given. The proposed method is found to perform comparable to a prediction error method in a simple example.
On subspace system identification methods
Modeling Identification and Control, 2022
An open and closed loop subspace system identification algorithm DSR e is compared to competitive open loop algorithms, DSR, and N4SID. Additionally, DSR e is compared vs the optimal Prediction Error Method (PEM). Monte Carlo simulations with discrete random state space models are used for testing the subspace identification algorithms in the numerical simulation section.
Subspace state space system identification for industrial processes
Journal of Process Control, 2000
We give a general overview of the state-of-the-art in subspace system identi®cation methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basics of linear subspace identi-®cation are summarized. Dierent algorithms one ®nds in literature (such as N4SID, IV-4SID, MOESP, CVA) are discussed and put into a unifying framework. Further, a comparison between subspace identi®cation and prediction error methods is made on the basis of computational complexity and precision of the methods by applying them on 10 industrial data sets. #
Computing the Oblique Projection in Subspace-Based Multivariable System Identification
IFAC Proceedings Volumes, 1997
Recently proposed algorithms for mult.ivariable syst.em identification by subspace techniques involve the computation of the so-called "oblique projection" to estimat.e t.he system order and system matrices. The paper shows that this comput a-!.ion can be performed without. (lctually solving any least-squ(lre problems. and that ort.hogonal transformations only should be applied to the original input.-out.put dat.a sequences. Both det.erministic and combined deterministic-stochastic identification problems can be dealt with. Copyright© 1998 IFAC
IEEE Transactions on Signal Processing, 2000
The identification of multi-input multi-output (MIMO) linear systems has recently received a new impetus with the introduction of the state-space (SS) approach based on subspace approximations. This approach has immediately gained popularity, owing to the fact that it avoids the use of canonical forms, requires the determination of only one structural parameter, and has been empirically shown to yield MIMO models with good accuracy in many cases. However, the SS approach suffers from several drawbacks: There is no well-established rule tied to this approach for determining the structural parameter, and, perhaps more important, the SS parameter estimates depend on the data in a rather complicated way, which renders almost futile any attempt to analyze and optimize the performance of the estimator.
Journal of Computational and Applied Mathematics, 2004
We present a software package for structured total least-squares approximation problems. The allowed structures in the data matrix are block-Toeplitz, block-Hankel, unstructured, and exact. Combination of blocks with these structures can be specified. The computational complexity of the algorithms is O(m), where m is the sample size. We show simulation examples with different approximation problems. Application of the method for multivariable system identification is illustrated on examples from the database for identification of systems DAISY.
Efficient data processing for subspace-based multivariable system identification
IFAC Proceedings Volumes, 2004
Efficient, structure-exploiting techniques for input/output data processing in subspace-based multivariable system identification are investigated. The techniques are implemented in the system identification toolbox for discrete-time systems, SLIDENT, incorporated in the freely available Fortran 77 Subroutine Library in Control Theory (SLICOT). Besides drivers and computational routines, this toolbox provides MATLAB interfaces, implementing several algorithmic approaches. Extensive numerical testing and comparisons with similar MATLAB tools show that SLIDENT is reliable, efficient, and powerful enough to solve industrial identification problems.
1995
This paper deals with the analysis of a frequency domain identi cation algorithm. The algorithm identi es state-space models given samples of the frequency response given at equidistant frequencies. A rst order perturbation analysis is performed revealing an explicit expression of resulting transfer function perturbation. Stochastic analysis show that the estimate is asymptotically (in data) normal distributed and an explicit expression of the resulting variance is given. Monte Carlo simulations illustrates the validity of the variance expression also for the non-asymptotic case.