Robust Recursive Identification Research Articles

Robust Recursive Identification of ARX Models Using Beta Divergence

The robust recursive identification method of ARX models is proposed using the beta divergence. The proposed parameter update law suppresses the effect of outliers using a weight function that is automatically determined by minimizing the beta divergence. A numerical example illustrates the efficacy of the proposed method.

Recursive identification for Wiener non‐linear systems with non‐stationary disturbances

This study investigates the robust recursive identification problem for Wiener non-linear systems with non-stationary disturbance and measurement white Gaussian noise. Non-stationary disturbances cannot be eliminated by conventional statistical strategy. To overcome such problem, the non-stationary disturbance signal is modelled as a dynamic parameter with a small change rate which is to be estimated step. Utilising the forgetting factor (FF) and the auxiliary model strategy, a discrete-time recursive least-squares algorithm is designed by augmenting the parameter vector and the information vector. To facilitate the steady asymptotic convergence of the time-invariant system parameters and the dynamic tracking ability of the disturbance, two adaptive FFs are proposed to construct a new matrix FF scheme that is used to update the covariance matrix. Moreover, several asymptotic convergence conditions are also derived based on the stochastic statistical theory under persistent excitation condition. Finally, one illustrative example with non-stationary disturbance is employed to show the effectiveness and advantages of the proposed algorithms.

A statistical pattern recognition approach to robust recursive identification of nonstationary AR model of speech production system

We propose a new robust recursive procedure based on the weighted recursive least squares (WRLS) algorithm with variable forgetting factor (VFF) and frame-based quadratic classifier for identification of nonstationary AR model of speech. Two versions of the frame-based quadratic classifier design procedure are elaborated upon. Experimental results are obtained in analyzing speech signal on voiced and mixed excitation frames.

Robust pole placement control of a fermentor

This paper deals with robust pole placement control of a continuous flow alcoholic fermention process. The strain used for experiments is Saccharomyces cerevisae UG5. The fermentor is subject to changs in pH, temperature, mixing, etc. The regularized pole placement adaptive control algorithm is used for regulation and tracking purposes. The substrate concentration and the dilution rate have been respectively selected as controlled and control variables. The eliminant matrix associated to the pole placement problem is non-singular if the identified input-output model has common poles and zeros. Two solutions have been adopted to deal with this ill-conditioning problem. The first solution consists of monitoring the determinant of the eliminant matrix and the second consists of adding a correction term to the highest degree coefficient of either the numerator or denominator of the process transfer function. A robust recursive identification scheme is used for parameters estimation. The fermentor was interfaced with PC computer using a multitasking operating system. Experiments carried out with the fermentor, illustrate the use of the regularized pole placement adaptive control algorithm.

Convergence Analysis of a Robust Recursive Identification Method for Autoregressive Models

Recently the concept of robustness has attracted considerable attention of control engineers for several control problems. One of this direction is robust identification. Polyak and Tsypkin (1979, 1980) proposed a robust recursive identification method analogous to the recursive least squares method. It follows the idea of Huber's maximum-likelihood-type estimator (M-estimator), which seeks for a minimax solution, i.e., an estimator minimizing the maximum asymptotic variance over some prescribed convex class to which the underlying distribution of innovations belongs. Its convergence properties for dynamic system identification have not been discussed thoroughly because of the introduction of some approximations in the identification method and correlation between observations. In this paper, convergence analysis of the robust recursive identification method is discussed for autoregressive models. Two theorems on convergence properties of the robust identification method are presented and proved by using the ODE approach and martingale convergence theory.

Analysis of Robust Recursive Identification Algorithms

Abstract The problem of recursive robust identification of linear discrete-time dynamic stochastic systems is discussed. Supposing approximately Gaussian system disturbance samples, a general form of robustified recursive identification algorithms of stochastic approximation type, characterized by an adequate nonlinear residual transformation, is defined. In order to improve the convergence rate, especially on short data sequences, the weighting matrix of the algorithm is derived by performing step-by-step optimization of a predefined empirical criterion. The convergence of the estimates w.p.l. is established theoretically by using martingale theory. The theoretical results are followed by extensive Monte Carlo simulation results, providing a basis for making a precise judgement of real practical robustness of the algorithms. Important relationships between parameters describing the algorithms are pointed out.

Application of M-Estimation in Robust Recursive System Identification

A robust recursive identification algorithm, which is insensitive to large errors in data, is introduced. This is based on a well known robust statistical method called M-estimation. The convergence and efficiency of the proposed method are theoretically investigated. Simulated as well as real-life examples are also provided to substantiate the power of the new method in comparison with the existing methods.