Mathematical and cybernetical means of aed theory

Mathematical and cybernetical means of aed theory are considered in the paper. Unlike set theory based mathematics the new knowledge means are coherent with design and control and learning tasks requirements. They allow one to realize the main law of hierarchical level space: all units arise in lower levels multiplying and uniting, create more high levels units and are changed by higher levels. It is the law of new mathematics with units and actions which are changed when higher units and actions arise in lower actions carrying out. Aed processors and hierarchical knowledge networks created in agreement with this law (as well as the units and processes of all known levels: physical, chemical, biological, demographical, engineering and knowledge) are able to connect the diverse levels and to design their new states with taking into account their own changing constructions and activity and their interactions.