Background. Identification methods, as the methods of mathematical modeling of real dynamic systems subject to uncontrolled random noise are an important part of the process of solving control tasks nowadays. If the a priori information about the object is missing (or it needs to be confirmed), there are methods for determining the order of mathematical models of dynamic systems with noise in the input and output signal. But these methods are not able to answer all the questions about the peculiarities of the system and represent only some guidance in choosing a possible model. The aim of this work is to exam the algorithm of structural- parametric identification of LDS (linear dynamical systems) in the presence of observation noise in the input and output signals in the conditions of a priori uncertainty (unknown distribution law of interference).
Materials and methods. We propose a method of structural-parametric identification, which allows to estimate the order LDS without the use of a transfer function and impulse response of the system in the presence of interference monitoring of input and output signals. Structural identification problem formalized in the way that its decision coded in fixed length vector where each element corresponds to a shift signal input and output. Thus, the problem is reduced to solving the problem of integer programming which belongs to the class of NP-hard (nondeterministic polynomial time). For the problem of the choice of the structure of the numerical model there is an approach which is based on a genetic algorithm.
Results. As for the testing system we selected a model with the number of input variables x = 4, where the delay of the output for each x: r1 = 3, r2 = 1, r3 = 1, r4 = 2. The coefficients on the output b = [0,8; –0,5; 0,2] and the input of a = [0,4; –0,5; –1; 0,3; –0,2; 0,6; 0 , 4, –0.5, –1, 0.3, 0.2], the corresponding to rj shift for every x. The complexity of the system p = 9, and for all tests the total sample size N = 10000. In various signal-to-noise ratio on input and output, these methods are compared as a function of loss for parametric identification: the method of least squares, recursive method of instrumental variables and our developed criteria.
Conclusions. Based on the test results, we can conclude that: increase in the search space p more than the standard model and the increase of number of parameters, the error is reduced slightly. That is, if the changes are minor and the criteria values p do not lead to a noticeable reduction in error, then further steps to identify make no sense. And there is an advantage of the developed criterion that allows more precise parametric identification with noise at the input and the output. The developed approach allows to conduct structural and parametric identification of LDS arbitrary dimension of input and output models and for a finite time to specify accuracy thesaurus models, where each model meets the criterion of sustainability.
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