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Unit sliding mode control in infinite dimensional systems. (English) Zbl 0907.93015

The object of this paper is to develop sliding mode control design methods for infinite-dimensional systems. The unit control method was introduced for finite-dimensional systems by S. Gutman [IEEE Trans. Autom. Control AC-24, 437-443 (1979; Zbl 0416.93076)] and by S. Gutman and G. Leitman [|Optim. Tech., Part 2, Proc. 7th IFIP Conf., Nice 1975, Lect. Notes Comput. Sci. 41, 729-755 (1976; Zbl 0334.93030)]. Since the unit control has as advantage that it only changes on manifolds, it can be extended to infinite-dimensional spaces. This is in contrast with conventional component-wise control. The methods are illustrated by designing a control for heat and mechanical distributed processes operating under uncertainty conditions.
Reviewer: H.Zwart (Enschede)

MSC:

93B12 Variable structure systems
93C25 Control/observation systems in abstract spaces
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory