SOLVABILITY OF DIRECT AND INVERSE PROBLEMS IN THE CONTROL-THEORY OF DYNAMICAL-SYSTEMS

The oriented manifolds method [1,2] is developed for solving direct an d inverse problems of nonlinear dynamical systems. The controllability conditions are obtained as conditions of absence of special type solu tions of partial differential equations similar to Lyapunov - Levi-Civ ita equations, and General Stabilization Theorem has been proved. The solution of inverse problems is based on the construction of inverse s ystem and the case of using the set of trajectories is considered. The results obtained are applied to the control problems of rigid body mo tion by means of jet force and gyros with one and two degrees of freed om.