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Controllability criteria for time-delay fractional systems with a retarded state

100%
Sikora B.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 3
521-531
EN
The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
2
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On the constrained controllability of dynamical systems with multiple delays in the state

100%
Sikora B.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 4
469-479
EN
Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllability with constrained controls for dynamical systems with delays in the state are established. Various types of constraints are considered. Numerical examples illustrate the theoretical analysis. An example of a real technical dynamical system is given to indicate one of possible practical applications of the theoretical results.
3
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On constrained controllability of dynamical systems with multiple delays in control

100%
Sikora B.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 1
87-101
EN
Linear, continuous dynamical systems with multiple delays in control are studied. Their relative and absolute controllability with constrained control is discussed. Definitions of various types of constrained relative and absolute controllability for linear systems with delays in control are introduced. Criteria of relative and absolute controllability with constrained control are established. Constraints on control values are considered. Mutual implications between constrained relative controllability of systems with and without delays are studied as well as implications between constrained relative and absolute controllability of systems with delay in control. The results are illustrated by examples.
4
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Improving prediction models applied in systems monitoring natural hazards and machinery

63%
Sikora M., Sikora B.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 2
477-491
EN
A method of combining three analytic techniques including regression rule induction, the k-nearest neighbors method and time series forecasting by means of the ARIMA methodology is presented. A decrease in the forecasting error while solving problems that concern natural hazards and machinery monitoring in coal mines was the main objective of the combined application of these techniques. The M5 algorithm was applied as a basic method of developing prediction models. In spite of an intensive development of regression rule induction algorithms and fuzzy-neural systems, the M5 algorithm is still characterized by the generalization ability and unbeatable time of data model creation competitive with other systems. In the paper, two solutions designed to decrease the mean square error of the obtained rules are presented. One consists in introducing into a set of conditional variables the so-called meta-variable (an analogy to constructive induction) whose values are determined by an autoregressive or the ARIMA model. The other shows that limitation of a data set on which the M5 algorithm operates by the k-nearest neighbor method can also lead to error decreasing. Moreover, three application examples of the presented solutions for data collected by systems of natural hazards and machinery monitoring in coal mines are described. In Appendix, results of several benchmark data sets analyses are given as a supplement of the presented results.
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