Abstracts

Cybernetiks

In the report a recently discovered new phenomena is depicted. It was discovered at St. Petersburg State University. In special cases during equivalent transformations of mathematical models conventional usual and widely-used equivalent transformations substantially change the sensibility of solutions to variations of coefficients and parameters. They suddenly lead to serious errors and destroy the reliability of intervals computations even when intervals values are infinitely small in practice.

In the report ways of recovering the reliability of intervals computations results are given. They are based on the use of new conception (discovered in St.Petesburg University) of transformations that are equivalent in a widened sense. Primarily this phenomenon was discovered during the investigation of stability computation and stability reserves of control systems [1,2,3]. This discovery arose an acute discussion [4,5] since an unexpected meeting with special cases could have become (and became!)the cause of mistakes computations and could become causes of wrecks and catastrophes [3]. Later it has been discovered that these phenomena can be encountered in a lot of intervals computations.

Literature:

1. Petrov Yu.P. Optimal control systems synthesis when perturbing forces are not completely known. L. Leningrad University publication. 1987,289 pp.
2. Petrov Yu.P. Stability of linear systems at parameters variations. Automatics and telemechanics, 1994, ?11, pp.186-189.
3. Petrov Yu.P., Petrov L.Yu. Unexpected phenomena in mathematics and their connection with wrecks and catastrophes of recent years. St.Petersburg, 1999, 115 pp.
4. Gaiduk A.R. To the researching of the linear systems stability. Automatics and telemechanics, 1997, ?3, pp.153-160.
5. Academician Danilievich Ya.B., Petrov Yu.P. On the necessity of widening the conception of equivalence of mathematical models. Reports of The Science Academy. 2000, ?4, pp. 473-475.

Note. Abstracts are published in author's edition

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