Showing papers on "System identification published in 1968"

System Identification and the Principle of Random Contraction Mapping

Abstract: The problem of identifying a linear discrete system is considered where the input-output data is noise-corrupted. An iterative algorithm is suggested which converges in a statistical metric. This convergence is obtained through the principle of random contraction mapping.

Two stochastic approximation procedures for identifying linear systems

Abstract: A Robbins-Monro [1] stochastic approximation procedure for identifying a finite memory time-discrete time-stationary linear system from noisy input-output measurements is developed. Two algorithms are presented to sequentially identify the linear system. The first one is derived, based on the minimization of the mean-square error between the unknown system and a model, and is shown to develop a bias which depends only on the variance of the input signal measurement error. Under the assumption that this variance is known a priori, a second algorithm is developed which, in the limit, identifies the unknown system exactly. The case when the covariance matrix of the random input sequence is not positive definite is also considered.

System identification from noise-corrupted measurements

Abstract: A simple algorithmic solution is developed for the discrete time, nonlinear, system identification problem based on a stochastic approximation method. The method is applicable to the noisy, as well as the noiseless, input-output measurement case. A minimal statistical knowledge of the noise and input sequences is required for this method; also, the algorithm is very easy to program. The proof of convergence for the algorithm is given along with some experimental results obtained from some control system input-output data.

A review and discussion of some methods for system identification and modeling.

Abstract: Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computational techniques which use input-output data from physical systems to automatically construct mathematical models which, in some sense, provide the ‘best’ descritpions of the real systems. This paper briefly discusses a few of the more recent mathematical techniques available for model generation and testing. A new identification method based upon convex and linear programming is discussed in detail and a number of examples indicating its applicability are given. The linear programming method is basically an approximation to a convex programming problem, the solution of which determines the coefficients of the differential equation describing the observed system data. A number of extensions of the identification method indicate some of its most useful properties. The order of the assumed model differential equation can be larger than that of the unknown system and the identification process will either assign zero values to the superfluous coefficients of the model or pole-zero cancellations will occur in the factored form of the laplace transform of the model transfer function. ‘Best’ lowest order models may be selected automatically. Liner constraints among the coefficients of the model differential equation may be used to restrict the allowable ranges of the coefficients. Multiple sets of data for a single system may be used simultaneously in the indentification process. Multiple input-output systems or systems described by difference equations or with transportation lag can also be identified. Coefficients of time varying and/or nonlinear models may be determined.

Convergence of the quantizing learning method for system identification

Abstract: Sufficient conditions are presented for guaranteed convergence of the "quantizing method" system identification process, along with a comparison of the times of identification using the quantizing method and the fundamental method. This supplements a paper by Nagumo and Noda.

Reduction and identification of multivariable processes using regression analysis

Abstract: The paper is concerned with the application of multivariate regression analysis to the reduction of multivariable control problems and to the identification of linear and nonlinear time-varying processes. Reduction is performed by grouping the input and output variables of a many variable process into a small number of groups. Control is exercised in terms of a few variables, each representing such a group. Regression is further applied to the dynamic identification of reduced or unreduced linear and nonlinear multivariable processes where no a priori information of the dynamic characteristics is available. Both reduction and identification may be performed on-line. The resulting techniques are conveniently incorporated in control procedures based on dynamic programming and on predictive adaptation.

Analog methods for on-line system identification using noisy measurements.

Abstract: Nonlinear system on-line identification in presence of noise, using stochastic methods and analog equipment