Differential manifolds of the optimal solutions of a system of three ordinary equations

Abstract

Optimal synthesis of an ordinary differential equation with control consists in ascribing the motion laws determined by control values to the domains of a decomposition of the state space, that is in establishment of a space of optimal solutions, or in rendering a definite structure to this space. In the paper are presented the considerations relating to the properties of the optimal structure of a three-dimensional space. Necessary conditions of optimality have been given, in geometrical form, of a three-dimenisional differential equation.