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Abstrakty
This paper focuses on the connection between sliding motions and low frequency modes of high-gain feedback systems in an infinite dimensional framework. We study a particular class of abstract control systems in a Hilbert space setting and analyse their high-gain behaviour through singular perturbations. We show that the "slow" motion derived from the reduced model approximates the evolution of the closed loop after a fast transient. Moreover we prove a relation between this slow component of the high-gain feedback system and sliding motions, in the spirit, of the analogous result in the finite dimensional setting by Young, Kokotovic and Utkin (Young et al., 1977).
Czasopismo
Rocznik
Tom
Strony
33--50
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Dipartimento di Matematica Universita di Genova Via Dodecaneso, 35, 16146 Genova, Italy
Bibliografia
- Curtain, R.F.and Pritchard, A.J. (1978) Infinite Dimensional Linear System Theory. Lecture Notes in Control and Information Sciences 8, Springer-Verlag, Berlin-New York.
- Krĕın S.G. (1971) Linear differential equations in Banach space. Translations of Mathematical Monographs 29, AMS Providence.
- Lakshmikantham, V.and Leela, S. (1969) Differential and integral inequalities. Mathematics in Science and Engineering 55, Academic Press, New York-London.
- Levaggi, L. (2002a) Sliding modes in Banach spaces.Differential and Integral Equations15(2), 167–189.
- Levaggi, L. (2002b) Infinite dimensional systems sliding motions. European Journal of Control 8(6), 508–516.
- Orlov, Yu.V. (1983) Application of Lyapunov method in distributed systems.Automat. Remote Control 4, 22–28.
- Orlov, Yu.V. (2000) Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE Trans. Aut. Control 45(5), 834–843.
- Orlov, Yu.V.and Utkin, V.I. (1982) Use of sliding modes in distributed system control problems. Automat. Remote Control 9, 36–46.
- Orlov, Yu.V.and Utkin, V.I. (1987) Sliding mode control in infinite-dimensional systems. Automatica 23(6), 753–757.
- Orlov, Yu.V.and Utkin, V.I. (1998) Unit sliding mode control in infinite-dimensional systems. Appl. Math. Comput. Sci. 8(1), 7–20.
- Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44, Springer-Verlag, New York.
- Sontag, E.D. (1990) Mathematical Control Theory. Texts in Applied Mathematics 6, Springer-Verlag, New York .
- Utkin, V.I. (1990) Control of infinite-dimensional plants. In: A.S.I. Zinober,ed.,Deterministic Control of Uncertain Systems. Peter Peregrinus, London.
- Utkin, V.I. (1992) Sliding Modes in Control and Optimization. Communications and Control Engineering Series, Springer-Verlag, Berlin.
- Young, K.D., Kokotovíc P.V.and Utkin, V.I. (1977)A singular perturbation analysis of high-gain feedback systems. IEEE Trans. Aut. Control 22(6), 931–938.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0040