Influence of Noise on Process of Finding Extremum in Extreme Automatic Control Systems
DOI:
https://doi.org/10.64915/RADAP.2025.102.%25pKeywords:
white noise, extreme regulation system, signal-to-noise ratio (SNR), finding the extremum, error probabilityAbstract
The article considers several issues related to the functioning of discrete extreme control systems. Namely, the influence of noise in the measuring path of the extreme control system on the process of finding the extremum of the characteristics of the control object. White noise with a centered Gaussian distribution is used as a noise model. To organize the process of finding the extremum in discrete extreme control systems, it is necessary to measure the extreme characteristic of the control object. After the measurements, the results are compared and a decision is made on the direction of finding the extremum. The presence of noise in the measuring path of the extreme control system distorts the measurement results. Depending on the characteristics of the noise and the extreme characteristic of the control object, the results of comparing the measured values in each specific case may be correct or incorrect. In the case of an incorrect result of comparing the measured values of the extreme characteristic of the control object, an incorrect decision is made about the direction of finding the extremum. This leads to an increase in the time of finding the extremum. The article determines the maximum possible probability of making an incorrect decision about the position of the extremum. Various cases of noise influence on the results of measuring the extreme characteristic of an object, which are the cause of erroneous determination of the position of the extremum, are considered. The dependences of error probability in determining the position of the extremum on the noise variance and the steepness of the extreme characteristic of the control object are obtained. Various options for organizing the search for the extremum are considered, which allow reducing the probability of error. An algorithm for searching for the extremum in extreme control systems is proposed, which minimizes the probability of error in the process of searching for the extremum.
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Copyright (c) 2025 І. М. Кирпатенко, А. В. Мовчанюк, Н. В. Єзерський, Я. Л. Зінгер
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