Open AccessOn one control problem with disturbance and vectograms depending linearly on given sets
Author(s) -
В.И. Ухоботов,
В. Н. Ушаков
Publication year - 2020
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm200306
Subject(s) - mathematics , realization (probability) , disturbance (geology) , regular polygon , control theory (sociology) , function (biology) , bridge (graph theory) , space (punctuation) , control (management) , process (computing) , computer science , geometry , medicine , paleontology , statistics , artificial intelligence , evolutionary biology , biology , operating system
A control problem with a given end time is considered, in which the control vectograms and disturbance depend linearly on the given convex compact sets. A multivalued mapping of the phase space of the control problem to the linear normed space E is given. The goal of constructing a control is that at the end of the control process the fixed vector of the space E belongs to the image of the multivalued mapping for any admissible realization of the disturbance. A stable bridge is defined in terms of multivalued functions. The presented procedure constructs, according to a given multivalued function which is a stable bridge, a control that solves the problem. Explicit formulas are obtained that determine a stable bridge in the considered control problem. Conditions are found under which the constructed stable bridge is maximal. Some problems of group pursuit can be reduced to the considered control problem with disturbance. The article provides such an example.