The Dynamic Programming Method in Impulsive Control Synthesisстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The control synthesis problem is one of the central problems in modern control theory. Its so-
lution can be obtained in various classes of feedback controls. For example, in classical control
theory under a geometric constraint, the desired control ranges in the set of extreme points of the
constraint, so that the synthesized system is described by dierential equations with discontinu-
ous right-hand side [1]. Sometimes, control synthesis can be described with the use of \switching
surfaces" dividing the phase space into domains with continuous controls, while discontinuities
(\switchings") are allowed on these surfaces [2{4].
However, the solutions can have impulsive character in many applied problems, for example,
in aerospace systems with instantaneous motion corrections, in systems with communication con-
strains, and in logical-dynamical systems. Such solutions require controls of generalized type, which
consist of impulsive \delta functions" or their combinations with a bounded control. First program
solutions in the impulsive control problem were obtained in [5]. It was shown in [6] that, in a linear
impulsive problem, the number of jumps of an optimal control does not exceed the dimension of
the phase space.
Such problems were considered mainly from the viewpoint of program controls [4, 7, 8], while
the construction of a well-formalized theory of impulsive control synthesis still remains an open
problem. In the present paper, we show that dynamic programming methods can be applied to
impulsive control problems in which solutions are sought in the form of synthesizing strategies.
We consider linear systems, which permits one to combine the classical theory of distributions
with the theory of generalized (viscosity) solutions [9{11] of the corresponding quasi-variational
inequalities [12] of Hamilton{Jacobi{Bellman type. The suggested approach also permits one to
study problems with higher-order derivatives of delta functions [13].