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Random projections and hotelling's T² statistics for change detection in high-dimensional data streams

Ewa Skubalska-Rafajłowicz (2013)

International Journal of Applied Mathematics and Computer Science

The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of Rn . We examine the random projection method using artificial noisy image sequences as examples.

Realization of nonlinear input-output equations in controller canonical form

Arvo Kaldmäe, Ülle Kotta (2018)

Kybernetika

In this paper necessary and sufficient conditions are given which guarantee that there exists a realization of a set of nonlinear higher order differential input-output equations in the controller canonical form. Two cases are studied, corresponding respectively to linear and nonlinear output functions. The conditions are formulated in terms of certain sequence of vector spaces of differential 1-forms. The proofs suggest how to construct the transformations, necessary to obtain the specific state...

Reduced order controllers for Burgers' equation with a nonlinear observer

Jeanne Atwell, Jeffrey Borggaard, Belinda King (2001)

International Journal of Applied Mathematics and Computer Science

A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal...

Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra

Ülle Kotta, Palle Kotta, Miroslav Halás (2010)

Kybernetika

The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuous- and discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer...

Reduction of large circuit models via low rank approximate gramians

Jing-Rebecca Li, Jacob White (2001)

International Journal of Applied Mathematics and Computer Science

We describe a model reduction algorithm which is well-suited for the reduction of large linear interconnect models. It is an orthogonal projection method which takes as the projection space the sum of the approximate dominant controllable subspace and the approximate dominant observable subspace. These approximate dominant subspaces are obtained using the Cholesky Factor ADI (CF-ADI) algorithm. We describe an improvement upon the existing implementation of CF-ADI which can result in significant...

Routh-type L 2 model reduction revisited

Wiesław Krajewski, Umberto Viaro (2018)

Kybernetika

A computationally simple method for generating reduced-order models that minimise the L 2 norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the L 2 -optimal approximation. Two examples taken from the relevant literature show that the suggested techniques may lead to...

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