Problem of Minimizing the Scatter Range of Trajectories of a Controlled Object

A minimax control problem for a quasilinear controlled object is conidered. The dynamics of the controlled object includes two types of controls, one of which models the variable impact of perturbations acting on the controlled object. The second control is used to compensate for disturbing factors...

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Veröffentlicht in:Moscow University computational mathematics and cybernetics 2021, Vol.45 (3), p.109-113
1. Verfasser: Nikol’skii, M. S.
Format: Artikel
Sprache:eng
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Zusammenfassung:A minimax control problem for a quasilinear controlled object is conidered. The dynamics of the controlled object includes two types of controls, one of which models the variable impact of perturbations acting on the controlled object. The second control is used to compensate for disturbing factors and is a constant vector selected from a given compact set. The quality of the pair of controls is determined using a continuous function defined on the phase space. The maximum of this function is taken over the reachability set of the considered controlled object, which characterizes the scatter range of trajectories of the control system at a given time. This maximum depends on a constant control from a given compact set. The resulting marginal function must be minimized over the set of constant controls. The properties of this marginal function are studied, and the existence of its minimum on the set of constant controls is substantiated. In addition, sufficient conditions are found under which the marginal function under study has the Lipschitz property.
ISSN:0278-6419
1934-8428
DOI:10.3103/S0278641921030031