### Research algorithm of nonlinear systems of automatic control in stochastic conditions

**Published:**08.10.2014

**Authors:** Kyaw Thu Aung , Melnikov D.V.

**Published in issue: **#4(28)/2014

**DOI: **10.18698/2308-6033-2014-4-1270

**Category:** Information technology | **Chapter:** Automated control systems

The main purpose of the article is to present the algorithm of studying the devices whose dynamics is described by stochastic nonlinear differential equations. The research method is based on replacing the stochastic task with the equivalent family of deterministic problems, obtained by the methods developed that allow us to accurately calculate probabilistic characteristics of random processes in control systems. The research algorithm is highly universal due to the fact that the original mathematical model of control systems describes almost all major classes of systems. The algorithm imposes no restrictions on the stationarity and the laws of distribution of random signals and random control system parameters; allows us to calculate not only the torque characteristics, but also the probabilities. The accuracy of calculating probability characteristics is determined by the number of samples of random variables, defined in a deterministic way.

**References**

**[1]**Arsenyev G.N., Zaitsev G.F. Radioavtomatika. Chast 2. Teoriya diskretnykh i optimal’nykh sistem avtomaticheskogo upravleniya RES [Radioautomatics. Part 2. The theory of discrete optimal and automatic control systems RES]. Moscow, Science Press Publ., 2008, 480 p.

**[2]**Papoulis A. Probability, random variables and stochastic processes. 3rd ed., New York, McGraw-Hill Publ., 1991, 666 p.

**[3]**Pupkov K.A., Egupov N.D., Makarenkov A.M., Trofimov A.I. Teoriya i kompyuternye metody issledovaniya stokhasticheskikh sistem [Theory and computer methods of stochastic systems investigation]. Moscow, Fizmatlit Publ., 2003, 400 p.

**[4]**Pupkov K.A, Egupov N.D., Trofimov A.I. Metody teorii avtomaticheskogo upravleniya. [Methods of control theory]. N.D. Egupov, ed. Moscow, Bauman MSTU Publ., 1998, 562 p.

**[5]**Krylov V.I. Priblizhennoe vychislenie integralov [Approximate calculation of integrals]. Moscow, Nauka Publ., 1967, 500 p.

**[6]**Melnikov D.V., Kornyushin Yu.P. Nauka i obrazovanie - Science and education, 2006, pp. 232-235.