ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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

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