On a problem of control of trajectory bundles

M. S. Nikol'skii

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 35 (2025) no. 1, pp. 75-81

Résumé

Various problems of control of trajectory bundles constitute an important object of study in modern mathematical control theory. Such problems arise, for example, in studying the motion of a flow of charged particles, and also in the presence of incomplete information about the initial state of the controlled system. In the present article, for a nonlinear controlled object of a quite general form on a fixed time interval $[0,T]$, the problem of control of trajectory bundles with a non-single-point initial set is considered. On the reachable set at the moment $T>0$, the problem of maximization of a given continuous function is studied. This problem can be interpreted as a problem on the spread of trajectories of the controlled object. The corresponding maximum depends on the chosen admissible control $u(\cdot )$. In the article, the existence of a minimum on the set of admissible controls from this maximum is substantiated.

Détail

Keywords: controlled object, the bundle of trajectories, attainable set, functional