Multilevel decision theory arises to resolve the contradiction between
increasing requirements towards the process of design, synthesis,
control and management of complex systems and the limitation of the
power of technical, control, computer and other executive devices, which
have to perform actions and to satisfy requirements in real time. This
theory rises suggestions how to replace the centralised management of
the system by hierarchical co-ordination of sub-processes. All
sub-processes have lower dimensions, which support easier management and
decision making. But the sub-processes are interconnected and they
influence each other. Multilevel systems theory supports two main
methodological tools: decomposition and co-ordination. Both have been
developed, and implemented in practical applications concerning design,
control and management of complex systems. In general, it is always
beneficial to find the best or optimal solution in processes of system
design, control and management. The real tendency towards the best
(optimal) decision requires to present all activities in the form of a
definition and then the solution of an appropriate optimization problem.
Every optimization process needs the mathematical definition and
solution of a well stated optimization problem. These problems belong to
two classes: static optimization and dynamic optimization. Static
optimization problems are solved applying methods of mathematical
programming: conditional and unconditional optimization. Dynamic
optimization problems are solved by methods of variation calculus:
Euler- Lagrange method; maximum principle; dynamical programming.
