Hierarchy of the Control and Optimal-Control Structures

An axiomatic approach to determination and analysis of the control structures was proposed. Abstract mathematical structures enabling one to develop a metric approach to the general problem of optimal control and establish the optimality conditions were considered. A new structure, hierarchy of metrics, characterizing the control system in the sense of the optimal-control problem was shown to arise. The structure of the state space and its existence conditions were considered. The chosen approach enables one to obtain a new hierarchy of the basic control structures in terms of a particular system of axioms.