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Iterative Learning Control - monotonicity and optimization

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Owens D., Daley S.

International Journal of Applied Mathematics and Computer Science

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2008

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tom 18

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nr 3

279-293

EN

The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.

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Best constant approximants in Orlicz-Lorentz spaces

100%

Levis F. E., Cuenya H. H., Priori A. N.

Commentationes Mathematicae

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2008

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tom 48

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nr 1

EN

The best constant approximant operator is extended from an Orlicz-Lorentz space \(\Lambda_{w,\varphi}\) to the space \(\Lambda_{w,\varphi'}\), where \(\varphi'\) is the derivative of \(\varphi\). Monotonicity property of its extension is established.

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Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals

63%

Czerwińska M. M., Kaminska A. H.

Commentationes Mathematicae

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2017

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tom 57

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nr 1

EN

This is a review article of geometric properties of noncommutative symmetric spaces of measurable operators \(E(\mathcal{M},\tau)\), where \(\mathcal{M}\) is a semifinite von Neumann algebra with a faithful, normal, semifinite trace \(\tau\), and \(E\) is a symmetric function space. If \(E\subset c_0\) is a symmetric sequence space then the analogous properties in the unitary matrix ideals \(C_E\) are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss the properties of general singular value function, submajorization in the sense of Hardy, Littlewood and Pólya, Köthe duality, the spaces \(L_p\left(\mathcal{M},\tau\right)\), \(1\leq p < \infty\), the identification of \(C_E\) and \(G(B(H), \operatorname{tr})\) for some symmetric function space \(G\), the commutative case when \(E\) is identified with \(E(\mathcal{N}, \tau)\) for \(\mathcal{N}\) isometric to \(L_\infty\) with the standard integral trace, trace preserving \(*\)-isomorphisms between \(E\) and a \(*\)-subalgebra of \(E\left(\mathcal{M},\tau\right)\), and a general method for removing the assumption of non-atomicity of \(\mathcal{M}\). The main results on geometric properties are given in separate sections. We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, \(k\)-extreme points and \(k\)-convexity, (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec−Klee properties, Banach−Saks properties, Radon−Nikodym property and stability in the sense of Krivine−Maurey. We also state some open problems.

Ograniczanie wyników

2 Commentationes Mathematicae

1 International Journal of Applied Mathematics and Computer Science

1 Cuenya H. H.

1 Czerwińska M. M.

1 Daley S.

1 Kaminska A. H.

1 Levis F. E.

1 Owens D.

1 Priori A. N.

1 2017

2 2008

Iterative Learning Control - monotonicity and optimization

Best constant approximants in Orlicz-Lorentz spaces

Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals