SUMMARY
A method has been proposed for the structural functional-cost modeling of a complex hierarchical system. The initial data for carrying out calculations directly based on the functional-cost model have been determined. We have proposed and substantiated the cost description of a complex system and its components by using analytical approximating dependences. An example of the functional-cost algorithm has been given that employs a Lagrange multiplier method for complex systems with a serial combination of its separate parts. The solution to the example is the distribution among the desired probabilities of the effective operation of individual parts in terms of the minimum cost. Deriving such distribution does not require absolute values of the cost of both parts and the entire system. The issues addressed in the cost rationalization include the following: ensuring the predefined level of the functional perfection of a system at its minimum cost; determining the minimum required level of functional excellence in a single link at the known levels of functional excellence of the system and all other links except the one under investigation; determining the required number of parallel operating links for the same purpose; clarification of the required level of the functional perfection of links (information sensors, information processing links, communication channels) that have parallel communication; the structural improvement of a complex system by selecting a link within the system for which the improvement of functional perfection can be realized at minimum cost. We have proposed rules for the structural rationalization of a complex system. The first of them is the rule of the rational structural structure of a complex system. That makes it possible to receive a sufficient benefit from the complex system at minimum cost. The second rule is the expediency of complicating a complex system. According to it, complicating a complex system is advisable only if it improves the functional perfection of the entire complex system. The third rule, a rule of the proper structure, shows that there are no unnecessary links in the complex system, that is, those links that do not perform any activities that are not functionally required by a given system