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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
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