V.N. Ushakov, V.I. Ukhobotov, I.V. Izmest’ev. On a problem of impulse control under a disturbance and a possible breakdown ... P. 249-263

We consider a linear problem with impulse control under an uncontrolled disturbance. The only information available about the disturbance is a connected compact set of its possible values. It is believed that one breakdown may occur and lead to a change in the dynamics of the controlled process. The time of the breakdown is not known in advance. Only the length of a time interval required to eliminate the breakdown is known. The goal of the control process is to ensure that the value of a linear function of the phase coordinates at a fixed point in time belongs to a given closed interval. The control is constructed based on the principle of minimizing the guaranteed result. The opponents are the disturbance and the time of the breakdown. Sufficient conditions are found under which the problem has a solution. A guaranteeing control is constructed.

Keywords: control, impulse control, disturbance, breakdown

Received February 1, 2021

Revised March 1, 2021

Accepted March 15, 2021

Funding Agency: This work was supported by the Russian Science Foundation (project no. 19-11-00105).

Vladimir Nikolaevich Ushakov, Dr. Phys.-Math. Sci., Corresponding Member of the Russian Academy of Sciences, Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: ushak@imm.uran.ru

Viktor Ivanovich Ukhobotov, Dr. Phys.-Math. Sci., Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Head of Department, Chelyabinsk State University, Chelyabinsk, 454001 Russia, e-mail: ukh@csu.ru

Igor’ Vyacheslavovich Izmest’ev, Cand. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Researcher, Chelyabinsk State University, Chelyabinsk, 454001 Russia, e-mail: j748e8@gmail.com

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Cite this article as: V.N. Ushakov, V.I. Ukhobotov, I.V. Izmest’ev. On a problem of impulse control under a disturbance and a possible breakdown, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 2, pp. 249–263;  Proceedings of the Steklov Institute of Mathematics (Suppl.), 2021, Vol. 315, Suppl. 1, pp. S236–S249.