Identification Of Stochastic Systems Research Articles

The Hammerstein–Wiener Model for Identification of Stochastic Systems

Identification of nonlinear stochastic systems in the class of Hammerstein–Wiener models is studied. The problem is specific due to the nonlinearities of the investigated object. Hammerstein–Wiener models are constructed with regard for the disturbances of the type of white noise and martingale sequence at the output of the object. A two-stage recursive identification algorithm is designed. Necessary and sufficient conditions for the strong consistency of parameter estimates found by this algorithm are formulated. The results are applied to adaptive tracking of the output of an object.

Hammerstein Models for Identification of Stochastic Systems

Identification of nonlinear stochastic systems in the class of Hammerstein models is investigated with regard for the nonlinearities of the investigated object. Hammerstein models are constructed with regard for the output noise in the form of a martingale sequence and moving mean are constructed. Necessary and sufficient conditions for the strong consistency of estimates of parameters of stochastic gradient algorithms are formulated. Their convergence rates are estimated. The results are applicable to adaptive tracking of the output of an object.

Structural and Parametric Identification of Stochastic Systems and Their Interconnections on the Basis of Petri Networks

Structural and parametric identification of stochastic systems of a variable random structure in terms of Petri networks is considered, the frequency method being used. Random parameters are described in terms of these nets. To reduce the complexity of the algorithms of analysis of a net model we have proposed the notion of a marking matrix. The resources of a net model for construction of the optimal plan of an experiment are clarified.

A new identification approach for FIR models

The identification of stochastic discrete systems disturbed with noise is discussed in this brief. The concept of general prediction error (GPE) criterion is introduced for the time-domain estimate with optimal frequency estimation (OFE) introduced for the frequency-domain estimate. The two estimation methods are combined to form a new identification algorithm, which is called the empirical frequency-domain optimal parameter (EFOP) estimate, for the finite impulse response (FIR) model interfered by noise. The algorithm theoretically provides the global optimum of the model frequency-domain estimate. Some simulation examples are given to illustrate the new identification method.

Identification of Continuous-time Time-varying Stochastic Systems via Distribution-based Approach

Identification of Continuous-time Time-varying Stochastic Systems via Distribution-based Approach

Identification of Hammerstein Nonlinear Stochastic Systems

Identification of Hammerstein stochastic dynamic systems is investigated. For this problem, the nonlinearities of the system must be taken into account. The solution is derived by recurrent gradient identification algorithms based on the Newton–Raphson and least-squares methods. Convergence is demonstrated, convergence rate is estimated, and parameter estimation accuracy is derived. The procedure is shown to be effective in practice.

Using Informational Measures of Dependence in Statistical Linearization

Some problems arising in identification of stochastic systems due to using nonlinear measures of dependence of random variables (processes) were analyzed. Recent publications describing approaches based on a consistent measure of dependence such as the mutual information were discussed. A constructive procedure of creating the linear input-output model that is statistically equivalent to the nonlinear dynamic stochastic system with white-noise Gaussian input process was proposed. The condition for coincidence of the mutual information of the input and output processes of the system and the mutual information of the input and output processes of the model which is used as a criterion for statistical linearization is pivotal to this procedure. This approach enables one to establish explicit relations defining the weight coefficients of the linearized model without using the unrealistic—in the context of identification—i>a priori condition for knowledge of the joint distribution of the output processes of system and model.

Subspace identification for continuous-time stochastic systems via distribution-based approach

This paper presents a novel approach for system identification of continuous-time stochastic state space models from random input–output continuous data. The approach is based on the introduction of random distribution theory in describing (higher) time derivatives of stochastic processes, and the input–output algebraic relationship is derived which is treated in the time-domain. The efficacy of the approach is examined by comparing with other approaches employing the filters.

The Application of Moment Method for Parameter Identification of Stochastic Systems

A moment method for parameter identification of stochastic systems is examined. Parameters of stochastic differential equations are defined from a solution of moment equations. Simple formulae are obtained for parameters of second order stochastic differential equation with linear damping and nonlinear restriction. These formulae are derived from a stationary solution of moment equations for first, second, third and fourth order moments. Some calculations by these formulae are presented.

On-line identification and adaptive trajectory tracking for nonlinear stochastic continuous time systems using differential neural networks

Identification of nonlinear stochastic processes via differential neural networks is discussed. A new “dead-zone” type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis the stability conditions for the identification error as well as for the neural network weights are established. The adaptive trajectory tracking using the obtained neural network model is realized for the subclass of stochastic completely controllable processes linearly dependent on control. The upper bounds for the identification and adaptive tracking errors are established.

Identification of unstable and nonminimum-phase stochastic systems

This paper proposes a recursive algorithm estimating coefficients of the linear stochastic control system (ARX system) driven by a martingale difference sequence, while adaptively stabilizing the system without introducing external excitation signal. The system is allowed to be unstable and of nonminimum-phase. The estimates derived for the coefficients of both closed-loop and open-loop systems are strongly consistent.

Subspace-based Identification for Continuous-Time Stochastic Systems via Distribution-Theoretic Approach

This paper presents a novel approach for system identification of continuous-time stochastic state space models from random input-output continuous data. The approach is based on the introduction of the random distribution theory in describing the (higher) time derivatives of stochastic processes, and the input-output algebraic relationship is derived which is treated in the time-domain. The efficacy of the approach proposed is examined by comparing with other approaches employing the filters.

Subspace-based identification for continuous-time stochastic systems via distribution-theoretic approach

Subspace-based identification methods have recently been attracted much attention and active researches for the algorithm of discrete-time stochastic systems are done, and our interest turns to identifying the continuous-time systems. In this paper, we propose a new method to handle the continuous-time stochastic systems in the subspace identification algorithm. Our proposed method uses the concept of the random distribution and describes the derivatives of the (non-differentiable) white Gaussian noise process in the sense of distribution. Then, we construct the input-output algebraic relationship by using the differential information date. Furthermore, signal subspace and quadruple system matrices ( A, B, C, D ) were derived by the algorithm based on subspace framework, and an illustrative numerical example is provided.

Subspace-based Identification of Continuous-Time Stochastic Systems via Random Distribution Approach

Subspace-based Identification of Continuous-Time Stochastic Systems via Random Distribution Approach

On least‐squares identification of stochastic linear systems with noisy input–output data

On least‐squares identification of stochastic linear systems with noisy input–output data

Comments on "On a least-squares-based algorithm for identification of stochastic linear systems"

The bias-eliminated least squares estimator proposed in the paper by Zheng (see ibid., vol.46, p.1631-8, 1998) is shown to be identical to a simple instrumental variable estimator, using delayed input values as instruments.

Real-time automated detection and quantitative analysis of seizures and short-term prediction of clinical onset.

We describe an algorithm for rapid real-time detection, quantitation, localization of seizures, and prediction of their clinical onset. Advanced digital signal processing techniques used in time-frequency localization, image processing, and identification of time-varying stochastic systems were used to develop the algorithm, which operates in generic or adaptable "modes." The "generic mode" was tested on (a) 125 partial seizures (each contained in a 10-min segment) involving the mesial temporal regions and recorded using depth electrodes from 16 subjects, and (b) 205 ten-minute segments of randomly selected interictal (nonseizure) data. The performance of the algorithm was compared with expert visual analysis, the current "gold standard." The generic algorithm achieved perfect sensitivity and specificity (no false-positive and no false-negative detections) over the entire data set. Seizure intensity, a novel measure that seems clinically relevant, ranged between 35.7 and 6129. Detection was sufficiently rapid to allow prediction of clinical onset in 92% of seizures by a mean of 15.5 s. This algorithm, which was implemented with a personal computer, represents a definitive step toward rapid and accurate detection and prediction of seizures. It may also enable development of intelligent devices for automated seizure warning and treatment and stimulate new study of the dynamics of seizures and of the epileptic brain.

On a least-squares-based algorithm for identification of stochastic linear systems

A new form of bias-eliminated least-squares (BELS) algorithm is developed to identify transfer function parameters of a linear time-invariant system, irrespective of noise dynamics. Unlike the BELS estimator previously presented, the main feature with the developed algorithm is that the transfer function parameters are consistently estimated in such a direct way that there is no need to prefilter observed data or to deal with a high-order augmented system. This greatly simplifies implementation of the BELS-based algorithms and reduces numerical efforts, whereas a desirable estimation accuracy can still be achieved. Two simulation examples are presented that clearly illustrate the good performances of the developed algorithm, including its superiority over one type of simple instrumental variable method.

Counterexample to General Consistency of Subspace System Identification Methods

Subspace methods for identification of linear dynamical systems consist of two main steps. First, a so-called subspace estimate is constructed. This usually corresponds to estimating the range space of the extended observability matrix. Then, the system parameters are estimated from the subspace estimate. The main objective of this paper is to show that subspace methods for the identification of combined deterministic and stochastic systems may fail to provide a consistent estimate of the subspace. Hence, for certain systems, the transfer function model estimated using the subspace identification algorithms is not a consistent estimate of the true system.

Subspace-based Identification of Stochastic Systems Using Innovation Model

Abstract In this paper a 4SID algorithm is proposed to identify a class of linear stochastic systems from the noisy input-output data sequence. First, the standard linear stochastic models are replaced equivalently by the innovations representation of Kalman filter equation. Then, by introducing a quasi-stationarity assumption for the error covariance matrix associated with the Kalman filter, our 4SID algorithm is derived. Finally, by simulation studies the effectiveness of our algorithm is shown.