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Inversion d’un opérateur de Toeplitz tronqué à symbole matriciel et théorèmes-limite de Szegö

Jean Chanzy (2006)

Annales mathématiques Blaise Pascal

Ce travail est une étude théorique d’opérateurs de Toeplitz dont le symbole est une fonction matricielle régulière définie positive partout sur le tore à une dimension. Nous proposons d’abord une formule d’inversion exacte pour un opérateur de Toeplitz à symbole matriciel, démontrée au moyen d’un théorème établi en annexe et donnant la solution du problème de la prédiction relatif à un passé fini pour un processus stationnaire du second ordre. Nous établissons ensuite, à partir de cet inverse, un...

Inversion in indirect optimal control of multivariable systems

François Chaplais, Nicolas Petit (2008)

ESAIM: Control, Optimisation and Calculus of Variations

This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.

Iterative estimators of parameters in linear models with partially variant coefficients

Shaolin Hu, Karl Meinke, Rushan Chen, Ouyang Huajiang (2007)

International Journal of Applied Mathematics and Computer Science

A new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable and...

Iterative learning control for over-determined under-determined, and ill-conditioned systems

Konstantin Avrachenkov, Richard Longman (2003)

International Journal of Applied Mathematics and Computer Science

This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. The Tikhonov regularization technique is discussed for computing the pseudoinverse to handle numerical instability. It is shown that for...

Iterative Learning Control - monotonicity and optimization

David H. Owens, Steve Daley (2008)

International Journal of Applied Mathematics and Computer Science

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...

IT/IS security management with uncertain information

Cyril Klimeš, Jiří Bartoš (2015)

Kybernetika

The paper introduces a novel proposal of a security management system destined primarily for application in the field of IT. Its core is formed by a triplet of cooperating knowledge-based (expert) systems, the knowledge bases of which consist of vague If-Then rules. The knowledge bases were created by experts on the problem domain and multiple times tested and verified on actual scenarios and real systems. With the system, a comprehensive methodology that is a part of a more complex approach to...

J-energy preserving well-posed linear systems

Olof Staffans (2001)

International Journal of Applied Mathematics and Computer Science

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems:...

Joint queue-perturbed and weakly coupled power control for wireless backbone networks

Thomas Otieno Olwal, Karim Djouani, Okuthe P. Kogeda, Barend Jacobus van Wyk (2012)

International Journal of Applied Mathematics and Computer Science

Wireless Backbone Networks (WBNs) equipped with Multi-Radio Multi-Channel (MRMC) configurations do experience power control problems such as the inter-channel and co-channel interference, high energy consumption at multiple queues and unscalable network connectivity. Such network problems can be conveniently modelled using the theory of queue perturbation in the multiple queue systems and also as a weak coupling in a multiple channel wireless network. Consequently, this paper proposes a queue perturbation...

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