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 Ufimsk. Mat. Zh., 2009, Volume 1, Issue 4, Pages 67–77 (Mi ufa32)

Re-determination motion in sliding mode by using feedback

S. A. Kochetkov, S. A. Krasnova, V. A. Utkin

Institute of Control Sciences, Russian Academy of Sciences

Abstract: The control objects described by differential equation with discontinuous right-hand side are considered in the paper. The sliding mode can arise in the state space of the system, when control inputs are realized by means of ideal relay. The regularization of system behavior is not trivial problem in sliding mode, because righthand side of differential eqation is not fulfilled Lipshitz and Caratheodory conditions. The new method of regularization of sliding mode motion is proposed in the paper. The main idea consists in taking into account nonlinearities of relay and using highgain feedback. It is shown that width of nonlinear zone of relay can be parametrized by gain coefficients of feedback. The regularization of motion in sliding mode is obtained with gain coefficients tends to infinity.

Keywords: differential equation with discontinuous right hand side, sliding mode control, regularization of the problem.

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Bibliographic databases:
UDC: 62-50

Citation: S. A. Kochetkov, S. A. Krasnova, V. A. Utkin, “Re-determination motion in sliding mode by using feedback”, Ufimsk. Mat. Zh., 1:4 (2009), 67–77

Citation in format AMSBIB
\Bibitem{KocKraUtk09} \by S.~A.~Kochetkov, S.~A.~Krasnova, V.~A.~Utkin \paper Re-determination motion in sliding mode by using feedback \jour Ufimsk. Mat. Zh. \yr 2009 \vol 1 \issue 4 \pages 67--77 \mathnet{http://mi.mathnet.ru/ufa32} \zmath{https://zbmath.org/?q=an:1240.34030}