Informatica

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).

In the previous paper (Pupeikis, 2000) the problem of closed-loop robust identification using the direct approach in the presence of outliers in observations have been considered. The aim of the given paper is a development of the indirect approach used for the estimation of parameters of a closed-loop discrete-time dynamic system in the case of additive correlated noise with outliers contaminated uniformly in it. To calculate current M-estimates of unknown parameters of such a system by means of processing input and noisy output observations, obtained from closed-loop experiments, the recursive robust 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.

In the papers (Pupeikis, 1988a, b; 1989a, b, c) the problems of efficiency determination, stopping and increase of the effectiveness of asymptotically optimal recursive algorithms are considered respectively by means of estimating time delay in an object and also introducing their robust analogues, stable to outliers in observations. The aim of the given paper is the development of the robust method for a determination of the model order on the basis of determinant ratio. The three methods forming the initial moment matrices are considered. By the first method the elements of the matrix, being the corresponding values of the sample covariance and cross-covariance functions, are calculated by classical formulas. In the case of the second method the same elements are substituted by their robust analogues. The third method is based on an application of auxiliary variables. The results of numerical simulation on a computer (Table 1) indicate the advisability to apply the robust method for determining the model order in the presence of outliers.