Stabilization problems of some systems under integrally small perturbations

S.G.Shaginyan

Yerevan State University

Aleka Manukyana, 1, Yerevan, 375025, Armenia

 

Problems of stabilizations and optimum stabilization of the operated object are being observed, when integral small outraging forces act on the object for final time lag (outraging forces are chosen from class function integrable in the Lebesgue sense). It is Expected that minimized functional is signconstant, but moving the object becomes only to be firm on acting forces. The statement of the problem is given to stabilizations and optimum stabilization on acting forces.

For nonlinear operated object, which under some possible controlling influence allows the independent linear first integrals, sufficient conditions are brought to solubility of the problem about optimum stabilization on acting forces.

It is shown that if linear system is not wholly controlled, that in general under any controlling influence system does not become to be firm on acting forces. The class of functionals is determined, at minimization of which is possible to solve the problem to optimum stabilization on acting forces for not wholly operated systems. For such problems Lyapunov's optimum function and optimum controlling influence.

There is an example, which shows that the spent energy on the optimal stabilization generally is more, than under optimal stabilization on acting forces for this system.