Identification Of Time-varying Systems Research Articles

Competitive Parallel Identifiers in Adaptive Control of Nonstationary Stochastic Systems

The problem of identification of time-varying (linear) stochastic systems by parallel processing (through a bank of parallel adaptive filters) in application to adaptive control is addressed. The novel method, previously developed for adaptive signal estimation is in a straightforward manner adapted to self-tuning control. A simple discrete-time control-object model varying in correspondence with reasonable (in the Nyquist sense) changes in an analog prototype is considered in the simulation study. Results concerning applicability of the technique as well as its robustness to time-variability and tuning parameters are shown. An improvement regarding robustness to changes in the noise variance and to computational difficulties is also discussed.

On the identification of time-varying dynamic systems by nonparametric procedures

The problem of identification of the unknown time-varying parameter in linear dynamic systems is considered. Nearest-neighbor procedures, based on the estimation of the state and its derivative, are presented. No conditions concerning the functional form of the time-varying parameter of the systems are made. If the state of the system has s derivatives, then the rate of convergence of the algorithm is O(n/sup -(s-1)///sup (1+2s)/) in probability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive identification and control of time-varying stochastic systems using ‘semi-periodic’ functions

The modelling of time-varying systems is discussed and a description of parameter time variation containing 'fast' and 'slow' elements given. An adaptive identification and control algorithm is presented and stability and convergence results derived for a large class of time-varying systems.

Robust real-time algorithms for identification of linear multivariable time-varying systems

The paper presents a discussion on the problem of the robust real-time identification of linear multivariable time-varying dynamic systems working in a noisy environment. Two methodologically different approaches to the design of such algorithms are presented. The first is based on the one-step estimation, optimal in the sense of the minimal conditional mean-square error, combined with convenient approximations of the underlying error covariance matrix. The second is based on the general formulation of robustified stochastic approximation algorithms, characterized by a suitable non-linear transformation of normalized residuals. Particular algorithms are derived on the basis of step-by-step optimization with respect to the weighting matrix of the algorithm. Monte Carlo simulation results illustrate the discussion, and show the efficiency of the proposed robust algorithms in the presence of large disturbance realizations, the so-called outliers.

Parameter identification of time-varying system via generalized orthogonal polynomials

An effective method is presented of using generalized orthogonal polynomials (GOPs) for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials. It is based on the repeated integration of a differential equation and the integration operational matrix of the GOP which can represent all kinds of individual orthogonal polynomials. By expanding the state function and control function into a series of GOPs, the differential input-output equation is converted into a set of overdetermined linear algebraic equations. The unknown parameters are evaluated by using the least-squares method in conjunction with an orthogonal polynomial expansion. An example is given to illustrate the usefulness of the method and very satisfactory results are obtained.

Nonstationary learning characteristics of the LMS algorithm

Upper and lower bounding first-order linear recursions for the mean-squared error realized with the LMS algorithm subjected to a sequence of independent nonstationary training vectors are derived. These bounds coincide to give the exact evolution of mean-squared error for the problem of identification of a nonrecursive time-varying system with white-noise excitation. This leads to an exact formula for time-averaged mean-squared error that is used to study optimization of the step-size parameter for minimum time-average misadjustment. New results on dependence of the minimal step size and the minimum misadjustment on the degree of nonstationarity are obtained.

Restricted exponential forgetting in real-time identification

Identification of time-varying stochastic systems is examined from the Bayesian viewpoint. The questions of which piece of posterior information should be forgotten and of how to forget it are discussed thoroughly, taking into account the main drawbacks of the commonly used technique of exponential forgetting. A novel procedure of suppressing obsolete information is suggested, endowed with two important features. Firstly, it modifies only that piece of so-far accumulated information which is being innovated by the currently measured data. Secondly, it makes it possible to respect partial prior knowledge about the location and/or evolution of parameters in a unified manner. The contributions of the procedure are illustrated in the special case of linear Gaussian regression-type models. A slight, but surprisingly effective, modification of the recursive least-squares method is derived which ensures a high numerical reliability of parameter tracking even for poorly excited systems. Its properties are demonstrated by a simulation example.

Identification and model reduction of time-varying discrete-time systems

Linear, discrete, time-variable systems are considered, and an important class of uniform realizations is defined. The necessary and sufficient conditions for a pulse response to be uniformly realizable are obtained. Two model reduction schemes, one via balanced realizations and the other via Hankel matrix are proposed. The latter approach can be considered as an identification algorithm for the two-dimensional pulse response sequence h( k, i). It is shown that the two approaches yield an identical reduced model which is always asymptotically stable.

Application of the operational matrix of differentiation for the identification of time-varying linear systems using polynomial series

The operational matrix of differentiation is used for the parameter identificaton of a class of time-varying linear systems using polynomial series. The main advantage of this approach is that it does not require the introduction of the initial conditions of the system, as it becomes necessary with the use of the operational matrix of integration. In this way the resulting algorithm is considerably simpler. The operational matrix of a polynomial series transformation is also used and may transform a given orthogonal polynomial series into another. This matrix simplifies considerably the computation of the product and coefficient matrices required for the identification of time-varying systems. Several characteristic examples are considered for the illustration of the effectiveness of the method.

Identification of a single-variable linear time-varying system via generalized orthogonal polynomials

The effective generalized orthogonal polynomials (GOPs) expansion is applied to estimating the parameters of a single-input-single-output linear time-varying system. It is based on the integration operational matrix for GOPs, which can represent all kinds of individual orthogonal polynomial. Using the concept of GOP expansion for a state function and a control function, the differential input-output equation is converted into a set of overdetermined linear algebraic equations. The unknown parameters are evaluated by a weighted least-squares method. An illustrative example is given. Very accurate results are obtained.

Identification of MIMO time-varying stochastic systems with unknown dead times

This paper presents a new on-line procedure for identifying MIMO time-varying stochastic dynamic systems. It is based on a decomposition model derived from the state-space representation. This scheme gives an estimated model with a minimal number of parameters. The parameters of the MIMO system are identified from short records with unknown dead times. Extended recursive least-squares and fixed-lag smoothing identification algorithms are applied to identify the validity of the model structure. Artificial and hydrological records are used to illustrate the efficiency of the proposed procedure.

Spline space approximation method of identification for time-varying systems

In this paper, the notions of Schauder bases and decompositions for a Sobolev space are used as an approximation method for solving the identification problem of time-varying systems. This extends the results obtained by Chen (1983). A numerical approximation is discussed.

Identification of time-varying bilinear systems using legendre series

A new method using the operational properties of the integration and product of the Legendre series is presented for identifying the unknown parameters of time-varying bilinear systems from the input–output data. This approach is straightforward and convenient for digital computations. One computational example is provided to illustrate the utility of the method.

Recursive Identification of Nonstationary Random Processes and Systems

Identification of time-varying random processes and systems by adaptive filtering methods is considered. A method for the synthesis of a stochastic difference equation modeling the dynamics of unknown parameters is proposed. A priori information required for the construction of this equation consists of the choice of the basis of functions approximating time evolution of the parameters. A recursive algorithm for the model structure selection and for adaptive parameter estimation is presented. An example of parametric spectral analysis of nonstationary autoregressive process is given.

Parameter identification of lumped time-varying systems via shifted Chebyshev series

Important and clear-sighted operational properties of shifted Chebyshev series are fully applied to the identification of time-varying linear systems. An effective computational formulation, which is very straightforward and convenient for digital computations, is achieved, thereby greatly reducing the computational difficulty. Simulation results show the superiority of the proposed method.

Shifted-Chebyshev-series analysis and identification of time-varying bilinear systems

Shifted Chebyshev series are developed in this study to analyse and identify time-varying bilinear systems. Effective computational formulations, which are very straightforward and convenient for digital computations, are achieved. Consequently, the computational difficulty can be remarkably reduced. Two illustrative examples are given to demonstrate the superiority of the presently proposed method.

時変連続系の適応同定

時変連続系の適応同定

Fixed-lag smoothing in the identification of time-varying systems with unknown dead time

This paper considers a new application of fixed-lag smoothing algorithms for identification. It could be used online in conjunction with the extended recursive least-squares identification algorithm. This offers a scheme for identifying time-varying process models with unknown dead time from sampled input-output records. Application to short records with time-varying dynamics, where recursive algorithms without smoothing may not give a clear indication of the time variation, is of particular interest. Optimal Kalman-filter and fixed-lag smoothing algorithms are reviewed, and their computational requirements and stability in an identification context are examined. The most attractive measures of model structure obtained from identification algorithms are tested on artificial and real records. It is concluded that the innovation and adjoint variables are feasible and effective indicators for identifying model structure goodness.

Identification of time-varying linear systems using orthogonal functions

This paper considers the problem of identifying the parameters and initial conditions of systems described by linear differential equations with time-varying coefficients. A new approach is proposed which is based on the idea of using orthogonal functions to represent the input—output data, as well as the unknown time-varying parameters of the system. Using certain properties of the orthogonal functions, an algorithm is constructed which reduces the identification problem to that of solving a linear algebraic system of equations.

Real-time identification of time-varying systems by non-parametric algorithms based on Parzen kernels

Non-parametric algorithms, based on Parzen kernels, for the real-time identification of non-stationary systems are presented. Weak and strong pointwise convergence of identification procedures is s...