Informatica

The aim of the given paper is development of an approach based on reordering of observations to be processed for the extraction of an unmeasurable internal intermediate signal, that acts between linear dynamical and static nonlinear blocks of the Wiener system with hard-nonlinearity of the known structure. The technique based on the ordinary least squares (LS) and on data partition is used for the internal signal extraction. The results of numerical simulation and identification of a discrete-time Wiener system with five types of hard-nonlinearities, such as saturation, dead-zone, preload, backlash, and, discontinuous nonlinearity are given by computer.

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), 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).

The aim of the given paper is a development of the direct approach used for the estimation of parameters of a closed-loop discrete-time dynamic system in the case of additive noise with outliers contaminated uniformly in it (Fig. 1). To calculate M-estimates of unknown parameters of such a system by means of processing input and noisy output observations (Fig. 2), the recursive robust H-technique based on an ordinary recursive least square (RLS) algorithm is applied here. The results of numerical simulation of closed-loop system (Fig. 3) by computer (Figs. 4–7) are given.