Positional impulse and discontinuous controls for differential inclusion

Abstract

Nonlinear control systems presented in the form of differential inclusions with impulse or dis- continuous 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. © 2020, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.