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Approximation of positional impulse controls for differential inclusions
Ivan A. Finogenkoa, Alexander N. Sesekinbc a Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
c N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Abstract:
Nonlinear control systems presented as differential inclusions with positional impulse controls are investigated. By such a control we mean some abstract operator with the Dirac function concentrated at each time. Such a control (“running impulse”), as a generalized function, has no meaning and is formalized as a sequence of correcting impulse actions on the system corresponding to a directed set of partitions of the control interval. The system responds to such control by discontinuous trajectories, which form a network of so-called “Euler's broken lines.” If, as a result of each such correction, the phase point of the object under study is on some given manifold (hypersurface), then a slip-type effect is introduced into the motion of the system, and then the network of “Euler's broken lines” is called an impulse-sliding mode. The paper deals with the problem of approximating impulse-sliding modes using sequences of continuous delta-like functions. The research is based on Yosida's approximation of set-valued mappings and some well-known facts for ordinary differential equations with impulses.
Keywords:
positional impulse control, differential inclusion, impulse-sliding mode.
Citation:
Ivan A. Finogenko, Alexander N. Sesekin, “Approximation of positional impulse controls for differential inclusions”, Ural Math. J., 8:1 (2022), 43–54
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https://www.mathnet.ru/eng/umj160 https://www.mathnet.ru/eng/umj/v8/i1/p43
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Abstract page: | 55 | Full-text PDF : | 12 | References: | 12 |
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