Synthesis of impulse and fast controls under uncertaintyстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Among the applications motivating the modern
mathematical control theory, more attention is given
to synthesis problems whose solutions are feedback
controls. Such problems also arise in impulse control
systems. Recently, problems have been posed that
require solutions on short time intervals. Such solu
tions can be obtained in systems with controls treated
as distributions (generalized functions) admitting
higher derivatives of delta functions [1, 2].
Openloop control strategies for systems with ordi
nary impulse controls were considered in fundamental
works [3, 4], while impulses of high orders were used
in [5], where approaches were proposed for reducing
the solution to auxiliary problems with ordinary
impulses. It was also shown in [5] that there exists a
higher order generalized control that solves the two
point boundary value control problem in zero time.
These results were obtained for openloop control sys
tems without uncertainty.
The synthesis of impulse controls in problems
without uncertainty was addressed in [6] (for first
order impulses) and in [7] (in the general case), while
problems with uncertainty were considered in [8].
Since impulses are ideal elements, they can be imple
mented in practice by applying approximations based
on bounded functions. Such approximations of ideal
impulse controls are known as fast controls [9, 10].
In this paper, impulse and fast controls are
designed for a linear system with an unknown
bounded disturbance. For this purpose, we use the
dynamic programming method described in [11],
which is extended below to impulse controls. It is
proved that the corresponding value function, which is
used to find the desired control, is the solution of a
variational inequality of the Hamilton–Jacobi–Bell
man (HJB) type. As a result, we obtain an impulse
control strategy under uncertainty and propose a
method for designing fast controls as based on impulse
control functions.