STRUCTURAL PROPERTIES OF GUARANTEED CONTROL-ESTIMATION PROBLEMS FOR HIERARCHICAL SYSTEMS
Sergey Kruglikov
The paper deals with axiomatic description of hierarchical
systems, the choice of adequate statements of optimization
problems under uncertainty cite{Kurz06} for such systems, the
study of analogues of the basic structural properties (duality,
separation) that are obtained earlier for the control and
estimation problems in the operator form cite{Krug97}. The
mathematical formalism is motivated by applied research, including
the simulation of control of objects team motion cite{Kurz09}
and processes of decision making in organizational systems, that
are connected by the unity applied mathematics.
Algorithms of a priori designing routes for group objects to bypass the obstacles, that are
described by a system of non-convex, disconnected sets. In this
case the problems of guaranteed observation and a priori
preparation of cartographic information are analogues. The
optimal control problem solution depends on the particular
dynamics of objects of practical interest. Examples simulation
classes of systems, of obstacles and admissible routes are
presented.
Another realm of interest includes simulating procedures for
managing the modernization of the production of high-tech
engineering enterprizes. The adequacy of research in terms of
hierarchical systems is provided by the multilevel structure of
managed object.