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Metric entropy of convex hulls in Hilbert spaces

100%

Li W. V., Linde W.

Studia Mathematica

2000

tom 139

nr 1

29-45

Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), $T={t_1,t_2,...}$, $||t_j||≤a_j$, by functions of the $a_j$'s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences $(a_j)_{j=1}^∞$.

Precise small deviations in L 2 of some Gaussian processes appearing in the regression context

100%

Kirichenko A., Nikitin Y.

Open Mathematics

2014

tom 12

nr 11

1674-1686

We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.

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Fault tolerant control using Gaussian processes and model predictive control

88%

Yang X., Maciejowski J.

International Journal of Applied Mathematics and Computer Science

2015

tom 25

nr 1

133-148

Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably realistic examples drawn from flight control.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Open Mathematics

1 Studia Mathematica

1 Kirichenko A.

1 Li W. V.

1 Linde W.

1 Maciejowski J.

1 Nikitin Y.

1 Yang X.

1 2015

1 2014

1 2000

Wyniki wyszukiwania

Metric entropy of convex hulls in Hilbert spaces

Precise small deviations in L 2 of some Gaussian processes appearing in the regression context

Fault tolerant control using Gaussian processes and model predictive control