M. Verhaegen

Identification of composite local linear state-space models using a projected gradient search

An identification method is described to determine a weighted combination of local linear state-space models from input and output data. Normalized radial basis functions are used for the weights, and the system matrices of the local linear models are fully parameterized. By iteratively solving a non-linear optimization problem, the centres and widths of the radial basis functions and the system matrices of the local models are determined. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is described. It is pointed out that when the weights depend only on the input, the dynamical gradient calculations in the identification method are stable. When the weights also depend on the output, certain difficulties might arise. The methods are illustrated using several examples that have been studied in the literature before.

An indirect approach to closed-loop identification of Wiener models

A Wiener model is a nonlinear block oriented model with a linear time-invariant block followed by a static nonlinear block. This paper presents a method to identify Wiener models with a general disturbance configuration in closed-loop using the indirect approach. The method is applied to data generated by a nonlinear simulation model of high purity distillation column.

LPV subspace identification using a novel nuclear norm regularization method

It is well-known that recently proposed Linear Parameter-Varying (LPV) subspace identification techniques suffer from a curse of dimensionality leading to an ill-posed parameter estimation problem. In this paper we will focus on regularization methods to solve the parameter estimation problem. Tikhonov and TSVD regularization are conventional general-purpose regularization methods. These general-purpose regularization methods give preference to a solution with a small 2-norm. In principle many other types of additional information about the desired solution can be incorporated in order to stabilize the ill-posed problem. The main contribution of this paper is that we propose a novel regularization strategy for LPV subspace methods: the nuclear norm regularization method. By applying state-of-the-art convex optimization techniques, the method stabilizes the parameter estimation problem by including information on the desired solution that is specific to the (LPV) subspace identification scheme. We will conclude the paper with a summarizing comparison between the different regularization techniques.

Change detection in the dynamics with recursive subspace identification

We propose a tracking mechanism to follow time-variations in the dynamics of a linear system with a recursive identification of the PI-MOESP scheme. The proposed mechanism consists of change detection scheme followed by a re-initialization of the recursive calculations. The change detection is based on the least-squares interpretation of the calculation in the subspace scheme and detects whether the estimates of the recursive solution without exponential forgetting lies in the confidence interval of the estimates obtained with a second finite-window length solution to the least-squares problem. When a change has been detected, the estimate by the recursive implementation is re-initialized via the solution of a constrained least-squares problem. One numerical example is presented to illustrate that our change detection and reinitialization scheme can detect incipient changes in the system dynamics without detecting changes in input dynamics.

Residual models and stochastic realization in state-space identification

This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.

Nonlinear Identification of High Purity Distillation Columns

Abstract Multivariate high purity distillation columns present a number of challenging problems for both system identification and control due to their nonlinear and ill-conditioned nature. In this paper, we discuss the problem of identifying a nonlinear Wiener model for high purity distillation columns for the purpose of control. We first argue that such a model must be developed by performing a multivariate experiment in closed-loop, which is in stark contrast with the current industrial practice of single-input multi-output open-loop experiments. We then discuss the related design issues (e.g. the design of input reference signal) and how they may be tackled. Finally we present some identification results based on data obtained from a simulation model under realistic disturbance condition.

Identification of MIMO bilinear state space models using separable least squares

We present an algorithm to identify MIMO discrete-time bilinear state space models from input-output measurements. We estimate the system matrices by optimizing an output error criterion. This criterion depends linearly on some of the system matrices and nonlinearly on the others. Using the principle of separable least squares, we first solve for the matrices that enter nonlinearly and then obtain the others by solving a linear least squares problem. It is pointed out that subspace-based techniques can be used to estimate the order of the system and to compute initial estimates of the matrices that enter the criterion in a nonlinear way. The algorithm has been tested on a MIMO simulation example.

Subspace identification of multivariable LPV systems: a novel approach

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence. Ideas from closed-loop LTI subspace identification are used to formulate the input-output behavior of an LPV system. From this input-output behavior the LPV equivalent of the Markov parameters can be estimated. We show that with this estimate the product between the observability matrix and state sequence can be reconstructed and an SVD can be used to estimate the state sequence and consequently the system matrices. The curse of dimensionality in subspace LPV identification will appear and the kernel method is proposed as a partial remedy. The working of the algorithm is illustrated with two simulation examples.

Identification of Wiener models with process noise

Considers the identification of Wiener models whose LTI block includes a process noise contribution. We propose a three-step identification algorithm to solve this problem. The identification algorithm is based on a cross-correlation method and subspace identification.

Continuous-Time Subspace Model Identification Method Using Laguerre Filtering

Abstract This paper introduces a time domain subspace model identification method, for the identification of continuous-time MIMO state-space models. The measured signals are assumed to be contaminated with both process and measurement noise. The method uses a bilinear transformation on the data, to identify the system in an alternative domain. Afterwards the system is transformed back. An example of the method is presented.