An Extremal Step-by-step Realization of Sliding Regimes
Author(s):
D. V. Khlopin
khlopin@imm.uran.ru
Abstract:
A uniform approximation of sliding modes by piecewise-constant controls
is considered for a control differential system.
The linear growth condition and the assumption about the uniqueness
of solution of the equation of dynamics are not necessary for the system.
Two variants of the method of extremal aiming are investigated.
It is shown that
a method of A.V.Kryazhimskii approximates a general trajectory
of the bundle corresponding to the given sliding mode;
there exist sliding regimes which are not approximated
by trajectories generated by piecewise-constant controls;
if the right-hand side of the equation of dynamics
satisfies the condition of Kamke's general uniqueness theorem,
then an extremal method of N.N.~Krasovskii approximates each
sliding regimes.
This work was partially supported by RFBR, proj. 01-01-96-450
