The design and analysis of large and complex system requires frequently that
the system is divided into smaller units, called sub-systems. The structure of
overall system resulting from the interconnections of sub-systems can be very
complex. One of the most common structures, is the hierarchical structure,
i.e. the lay-out of the structure is vertical. Consequently in this report only
hierarchical systems are considered, and a special emphasis is put on twolevel
hierarchical systems. A diagram of a standard two-level hierarchical
system is shown in Fig. 12.1, where, as expected, two levels can be found,
namely the lower level and the upper level. The lower level consists of the
process level, where the process level has been divided into N sub-systems.
The sub-systems are connected to each other because there is either material
or information flows between these sub-systems. Each sub-system has its own
decision unit, which tries to control the behaviour of the sub-system so that
the objectives of this particular sub-system would be met. The decision unit
can also use feedback information from the sub-system to improve its ’control
policy’. However, quite often the objectives of the sub-systems are conflicting,
resulting in a poor overall performance. Hence an upper-level decision unit
or a coordinator has to be introduced, and the objective of this decision unit
is to coordinate the decision making of the sub-systems so that the overall
performance of the system would be improved. The coordinator receives
information from the sub-systems so that it can monitor the performance of
the overall system. Note that this approach is not as restrictive as it sounds,
because if a new higher level is added into a two-level system, in most of cases
the new level can be chosen to be the higher level of the modified system, and
the original two-level system becomes the lower-level of the modified system.