A. Kovalev, SOLVABILITY OF DIRECT AND INVERSE PROBLEMS IN THE CONTROL-THEORY OF DYNAMICAL-SYSTEMS, Zeitschrift fur angewandte Mathematik und Mechanik, 76, 1996, pp. 579-580
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.