CONTROL OF THE ENSEMBLE OF LINEAR TWO-PARAMETER DISCRETE SYSTEMS
https://doi.org/10.29235/1561-2430-2018-54-1-20-23
Abstract
The controllability of discrete systems with uncertainties is considered in this article. The concept of the ensemble of linear two-parameter discrete systems is introduced as a set of systems, whose coefficients belong to some given sets. The following problem is considered: for any initial state from the pre-assigned sets, one and the same control (universal control) is found for all ensemble systems reducing all solutions of these systems to a minimum zero neighborhood for finite time. In the case of interval uncertainty, finding the control is reduced to solving a nonlinear programming problem formulated in terms of the coefficients of the ensemble systems and the interval set of initial states. A constructive algorithm for building a desired control is proposed, an example is given.
About the Authors
I. V. Gaishun
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
D. Sc. (Physics and Mathematics), Director
Belarus
D. Sc. (Physics and Mathematics), Director
V. V. Goryachkin
Belarusian State University, Minsk
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor of the Applied Mathematics and Informatics Faculty
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor of the Applied Mathematics and Informatics Faculty
V. V. Krakhotko
Belarusian State University, Minsk
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor of the Applied Mathematics and Informatics Faculty
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor of the Applied Mathematics and Informatics Faculty
References
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2. Gaichun I. V., Goryachkin V. V., Krakhotko V. V. Estimate solutions to two-parameter discrete systems with interval coefficients. Vestsi Natsional’nai akademii nauk Belarusi. Ser. fiziko-matematicheskikh nauk = Proceedings of the National Aca demy of Sciences of Belarus. Physics and Mathematics series, 2014, no. 3, pp. 5–8 (in Russian).
3. Aschepkov L. T. Davydov D. A. Universal solutions of interval problems of optimization and control. Мoscow, Nauka Publ, 2006. 151 p. (in Russian).
4. Alefeld G., Herzberger J. Introduction to interval computations. Academic Press, 1983. 360 p.
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