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Approximate construction of the set of trajectories of the control system described by a Volterra integral equation
Author(s) -
Huseyin Nesir,
Guseinov Khalik G.,
Ushakov Vladimir N.
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300191
Subject(s) - mathematics , set (abstract data type) , volterra integral equation , trajectory , nonlinear system , affine transformation , integral equation , finite set , constraint (computer aided design) , mathematical analysis , pure mathematics , geometry , computer science , physics , quantum mechanics , astronomy , programming language
In this paper the set of trajectories of the control system is investigated. It is assumed that the behavior of the control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have an integral constraint. An approximation of the set of trajectories by the set which consists of a finite number of trajectories is given. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated.