Methodology and applied problems of the sustainable management in active systems

A concept of the sustainable management in arbitrary complex dynamical systems with human participation (active systems) is presented. It is noted that the sustainable development means satisfying the requirements of homeostasis and system consistency. The mathematical formalization of the problems of the sustainable management in active systems is based on the technique of differential games in a normal form, in a form of characteristic functions, and with hierarchical structure. The formulations of the sustainable management in active systems with independent agents, cooperative agents, and hierarchical control are given. The particular classes of incentive models and models of coordination of the social and private interests are considered. The review of several other applied problems solved in the frame of the proposed concept is given. An illustrative example is provided. The emphasis is placed on the methodical aspects of the developed concept.