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Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski — 2003

International Journal of Applied Mathematics and Computer Science

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested....

Control error dynamic modification as an efficient tool for reduction of effects introduced by actuator constraints

Krzysztof B. Janiszowski — 2009

International Journal of Applied Mathematics and Computer Science

A modification of digital controller algorithms, based on the introduction of a virtual reference value, which never exceeds active constraints in the actuator output is presented and investigated for some algorithms used in single-loop control systems. This idea, derived from virtual modification of a control error, can be used in digital control systems subjected to both magnitude and rate constraints. The modification is introduced in the form of on-line adaptation to the control task. Hence...

Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error

Krzysztof B. Janiszowski — 2014

International Journal of Applied Mathematics and Computer Science

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e.g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme,...

Identification of parametric models with a priori knowledge of process properties

Krzysztof B. JaniszowskiPaweł Wnuk — 2016

International Journal of Applied Mathematics and Computer Science

An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived and combined...

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