CONTROL OF AN ENSEMBLE OF LINEAR SYSTEMS WITH A DELAY IN CONTROL IN THE CLASS OF PIECEWISE CONSTANT FUNCTIONS

UDC 517.977

  • Goryachkin Vladimir Viktorovich – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Programming Technologies. Belarusian State University (4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus). E-mail: gorvv@bsu.by

  • Krakhotko Valeriy Vasil’yevich – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Optimal Control Methods. Belarusian State University (4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus). E-mail: krakhotko@bsu.by

  • Shirokanova Natalia Ivanovna – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of General Mathematics and Computer Science. Belarusian State University (4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus). E-mail: shirokanova@bsu.by

  • Ignatenko Vasiliy Vasil’yevich – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Higher Mathematics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: ihnatsenko@tut.by

DOI: https://doi.org/10.52065/2520-2669-2021-242-1-5-8

Keywords: system of differential equations, controllability, interval analysis, linear system with delay.

For citation: Goryachkin V. V., Krakhotko V. V., Shirokanova N. I., Ignatenko V. V. Control of an ensemble of linear systems with a delay in control in the class of piece-wise constant fnctios. Proseedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2021, no. 1 (242), pp. 5–8 (In Russian). DOI: https://doi.org/10.52065/2520-2669-2021-242-1-5-8.

Abstract 

For a linear system with a delay in control with constant interval coefficients (ensemble of systems), external estimates of solutions are obtained. The task of controllability of an ensemble is studied – the translation of a bundle of system trajectories from one n R set to another in a finite time in the class of piecewise constant controls. In the case of interval uncertainty the control finding is reduced to solving a linear programming problem formulated due to the ensemble systems coefficients Conditions for the controllability of an ensemble, which are presented in the form of an optimization problem, are proved. 

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References

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30.11.2020