Ivan A. Finogenko     (Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, 134 Lermontova Str., Irkutsk, 664033, Russian Federation)
Alexander N. Sesekin     (Ural Federal University, 19 Mira Str., Ekaterinburg, 620002; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108, Russian Federation)


Nonlinear control systems presented in the form of differential inclusions with impulse or discontinuous positional controls are investigated. The formalization of the impulse-sliding regime is carried out. In terms of the jump function of the impulse control, the differential inclusion is written for the ideal impulse-sliding regime. The method of equivalent control for differential inclusion with discontinuous positional controls is used to solve the question of the existence of a discontinuous system for which the ideal impulse-sliding regime is the usual sliding regime. The possibility of the combined use of the impulse-sliding and sliding regimes as control actions in those situations when there are not enough control resources for the latter is discussed.


Impulse position control, Discontinuous position control, Differential inclusion, Impulse-sliding regime, Sliding regime

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DOI: http://dx.doi.org/10.15826/umj.2020.2.007

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