Informatica

The aim of the given paper is the development of an approach for parametric identification of Wiener systems with piecewise linear nonlinearities, i.e., when the linear part with unknown parameters is followed by a saturation-like function with unknown slopes. It is shown here that by a simple data reordering and by a following data partition the problem of identification of a nonlinear Wiener system could be reduced to a linear parametric estimation problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. A technique based on ordinary least squares (LS) is proposed here for the estimation of parameters of linear and nonlinear parts of the Wiener system, including the unknown threshold of piecewise nonlinearity, too. The results of numerical simulation and identification obtained by processing observations of input-output signals of a discrete-time Wiener system with a piecewise nonlinearity by computer are given.

Least-squares method is the most popular method for parameter estimation. It is easy applicable, but it has considerable drawback. Under well-known conditions in the presence of noise, the LS method produces asymptotically biased and inconsistent estimates. One way to overcome this drawback is the implementation of the instrumental variable method. In this paper several modifications of this method for closed-loop system identification are considered and investigated. The covariance matrix of the instrumental variable estimates is discussed. A simulation is carried out in order to illustrate the obtained results.

In the previous papers (Pupeikis, 2000; Genov et al., 2006; Atanasov and Pupeikis, 2009), a direct approach for estimating the parameters of a discrete-time linear time-invariant (LTI) dynamic system, acting in a closed-loop in the case of additive noise with contaminating outliers uniformly spread in it, is presented. It is assumed there that the parameters of the LQG (Linear Quadratic Gaussian) controller are unknown, as well as known beforehand, too. The aim of the given paper is development of a minimum variance control (MVC) approach for a closed-loop discrete-time linear dynamic system when slowly or suddenly time-varying coefficients of the transfer function of such a system as well as that of a minimum variance (MV) controller are not known and ought to be estimated. The recursive parametric identification of an open-loop system and determination of the coefficients of the MV controller are performed in each current operation by processing observations in the case of additive noise at the output with contaminating outliers uniformly spread in it. The robust recursive technique, based on the S-algorithm, with a version of Shweppe's GM-estimator and with discounting previous data, used in the estimation, by introducing a constant as well as time-varying forgetting factors in the abovementioned estimator, is applied here in the calculation of estimates of the parameters of a dynamic system. Then, the recursive parameter estimates are used in each current iteration to determine unknown parameters of the MV controller. Afterwards, the current value of the MV control signal is found in each operation, and it is used to generate the output of the system, too. The results of numerical simulation by computer are presented and discussed.

In the previous papers (Pupeikis, 2000; Genov et al., 2006), a direct approach for estimating the parameters of a discrete-time linear time-invariant (LTI) dynamic system, acting in a closed-loop in the case of additive correlated noise with contaminating outliers uniformly spread in it, is presented. It is assumed here that the parameters of the LQG (Linear Quadratic Gaussian Control) controller are known beforehand. The aim of the given paper is development of a parametric identification approach for a closed-loop system when the parameters of an LTI system as well as that of LQG controller are not known and ought to be estimated. The recursive techniques based on an the M- and GM- estimator algorithms are applied here in the calculation of the system as well as noise filter parameters. Afterwards, the recursive parameter estimates are used in each current iteration to determine unknown parameters of the LQG-controller, too. The results of numerical simulation by computer are discussed.

The aim of the given paper is development of a joint input-output approach and its comparison with a direct one in the case of an additive correlated noise acting on the output of the system (Fig. 1), when the prediction error method is applied to solve the closed-loop identification problem by processing observations. In the case of the known regulator, the two-stage method, which belongs to the ordinary joint input-output approach, reduces to the one-stage method. In such a case, the open-loop system could be easily determined after some extended rational transfer function (25) is identified, including the transfer functions of the regulator and of the open-loop system, respectively, as additional terms. In the case of the unknown regulator, the estimate of the extended transfer function (27) is used to generate an auxiliary input. The form of an additive noise filter (36), that guarantees the minimal value of the mean square criterion (35), is determined. The results of numerical simulation and identification of the closed-loop system (Fig. 5) by computer, using the two-stage method and the direct approach are given (Figures 6–12, Table 1).