Active Parametric Identification of Gaussian Linear Discrete System Based on Experiment Design

Abstract

The application of methods of theory of experiment design for the identication of dynamic systems allows the researcher to gain more qualitative mathematical model compared with the traditional methods of passive identication. In this paper, the authors summarize results and oer the algorithms of active identication of the Gaussian linear discrete systems based on the design inputs and initial states. We consider Gaussian linear discrete systems described by state space models, under the assumption that unknown parameters are included in the matrices of the state, control, disturbance, measurement, covariance matrices of system noise and measurement. The original software for active identication of Gaussian linear discrete systems based on the design inputs and initial states are developed. Parameter estimation is carried out using the maximum likelihood method involving the direct and dual procedures for synthesizing A-and D-optimal experiment design. The example of the model structure for the control system of submarine shows the eectiveness and appropriateness of procedures for active parametric identication.Keywords: parameter estimation; maximum likelihood method; Kalman lter; experiment design; (Fisher) information matrix. IntroductionMathematical modelling is one of intensively developing scientic directions. Identication is an important element and the most dicult stage of the solution of the applied problem in various industries, transport, at calculation of systems of automatic control. In this regard development of software for parametrical identication models becomes especially important for fundamental science and practice.In terms of way of behavior present methods of identication can be divided into passive and active. In passive identication of dynamic systems only real operating signals and initial state are used in the modes of not disturbed operation [14].On the contrary, active identication assumes violation of technological mode and uses some special synthesized designs [59]. So, in a frequency method of parameter estimation of linear stationary models [10, 11] the signal represents the sum of harmonics which number doesn't exceed dimension of space. In this work optimal plan of experiment is searched during the extreme problem solution for some preliminary chosen functional of information (or covariance) vector-matrix of parameters to be estimated. The diculties connected with necessity of violation of a technological mode are provided by increase of eciency and correctness of research. Methods of active identication give to the The authors tried to generalize the results obtained in these papers and constructed new algorithms connected with the simultaneous design inputs and initial states.The questions of estimating the unknown parameters that we considered, together with the developed methods for designing experiments, enable us to achieve a general understanding of active identication.