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**Positional impulse and discontinuous controls for differential inclusion.**
*(English)*
Zbl 1461.93207

Summary: 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.

### MSC:

93C15 | Control/observation systems governed by ordinary differential equations |

93C27 | Impulsive control/observation systems |

93C10 | Nonlinear systems in control theory |

34A60 | Ordinary differential inclusions |

### Keywords:

impulse position control; discontinuous position control; differential inclusion; impulse-sliding regime; sliding regime
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\textit{I. A. Finogenko} and \textit{A. N. Sesekin}, Ural Math. J. 6, No. 2, 68--75 (2020; Zbl 1461.93207)

### References:

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