Control Under Indeterminacy and Double Constraintsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The present paper deals with control synthesis for a linear system subjected to indeterminate
perturbations. We assume that the control is constrained both geometrically and integrally, while
the noise is subjected only to a geometric condition. A similar statement of the problem was
considered in the paper [1], but it was assumed there that game is regular, which essentially
implies that the game problem can be reduced to an optimal control problem. In the present
paper, we consider the general case.
A doubly constrained control in the absence of indeterminacy was studied in [2, 3] and, in a
somewhat dierent statement (as the problem of damping of a linear system by a control that
simultaneously satises the minimum amplitude and the minimum energy expenditure conditions),
in [4{6]. A doubly constrained system can be treated as a system with a geometric constraint and
constrained phase coordinates [7{11].
We solve the problem by combining modied constructions of the Krasovskii extremal aim-
ing [12, 13] and the Pontryagin alternating integral [14{20]: the control synthesis is constructed as
a strategy extremal to the problem solvability set, which, in turn, is a limit of integral sums. In the
present paper, we use the terminology in [18, 21].