Opis

Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.

Aims and Scope: Archives of Control Sciences publishes papers in the broadly understood field of control science and related areas while promoting the closer integration of the Polish, as well as other Central and East European scientific communities with the international world of science.

ISSN

ISSN 1230-2384

Wydawcy

Committee of Automatic Control and Robotics PAS

1
A new method for computation of positive realizations of fractional linear continuous-time systems

Słowa kluczowe:
determination
positive
realization
transfer matrix
linear
continuous-time
fractional
system

A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

Słowa kluczowe:
multi-criteria group decision-making
aggregation operator
dual hesitant fuzzy numbers
Einstein operations
prioritized weighted averaging operator
prioritized weighted geometric operator

The purpose of this article is to develop a multicriteria group decision making (MCGDM) method in dual hesitant fuzzy (DHF) environment by evaluating the weights of the decision makers from the decision matrices using two newly defined prioritized aggregation operators based on score function to remove the inconsistencies in choosing the best alternative. Prioritized weighted averaging operator and prioritized weighted geometric operator based on Einstein operations are described first for aggregating DHF information. Some of their desirable properties are also investigated in details. A method for finding the rank of alternatives in MCGDM problems with DHF information based on priority levels of decision makers is developed. An illustrative example concerning MCGDM problem is considered to establish the application potentiality of the proposed approach. The method is efficient enough to solve different real life MCGDM problems having DHF information.

Słowa kluczowe:
q-rung orthopair fuzzy set
q-rung orthopair linguistic set
Heronian mean
q-rung orthopair linguistic Heronian mean
multi-attribute group decision making

The recently proposed q-rung orthopair fuzzy set (q-ROFS) characterized by a membership degree and a non-membership degree is powerful tool for handling uncertainty and vagueness. This paper proposes the concept of q-rung orthopair linguistic set (q-ROLS) by combining the linguistic term sets with q-ROFSs. Thereafter, we investigate multi-attribute group decision making (MAGDM) with q-rung orthopair linguistic information. To aggregate q-rung orthopair linguistic numbers ( q-ROLNs), we extend the Heronian mean (HM) to q-ROLSs and propose a family of q-rung orthopair linguistic Heronian mean operators, such as the q-rung orthopair linguistic Heronian mean (q-ROLHM) operator, the q-rung orthopair linguistic weighted Heronian mean (q-ROLWHM) operator, the q-rung orthopair linguistic geometric Heronian mean (q-ROLGHM) operator and the q-rung orthopair linguistic weighted geometric Heronian mean (q-ROLWGHM) operator. Some desirable properties and special cases of the proposed operators are discussed. Further, we develop a novel approach to MAGDM within q-rung orthopair linguistic context based on the proposed operators. A numerical instance is provided to demonstrate the effectiveness and superiorities of the proposed method.

Słowa kluczowe:
neutral system
Lyapunov matrix
Lyapunov functional

In the paper the parametric optimization problem for a linear system with two delays and a PD-controller is presented. In the parametric optimization problem the quadratic performance index is considered. The value of the quadratic index of quality is calculated due to the Lyapunov functional and is equal to the value of that functional for the initial function of the neutral system with two delays. The Lyapunov functional is determined by means of the Lyapunov matrix.

Słowa kluczowe:
bilinear systems
Hilbert spaces
ideal observability
observability subspace
delayed observation

An ideal observability subspace expression is stated for bilinear abstract system with bounded operator in Hilbert spaces. The case of finite dimentional space is also treated. However, it’s noticed that the state ideal observability can never be fulfilled within an infinite dimensional phase space in the case of scalar output. The case of bilinear discrete-time system with delays in observation is also described. To illustrate this work some examples are presented.

In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.

Słowa kluczowe:
fractional order controller
set-point weighting
2DOF PID
process control
unstable systems

The proportional-integral-derivative (PID) controllers have experienced series of structural modifications and improvements. Example of such modifications are set-point weighting and fractional ordering. While the former is to achieve two-degree-of-freedom (2DOF) ability of set-point tracking and disturbance rejection, the latter is to ensure smooth control action. Therefore, this paper reviews various forms of PID controllers and provides a comparative analysis of 2DOF PID and 2DOF fractional order PID (FOPID) controllers. The paper also discusses the conversion of one PID form to another. For the comparative analysis of the various controllers, a class of unstable systems are considered. Simulation result shows that in most cases the conversion from one form to another does not significantly affect the performance of the system. It is also observed that the 2DOF controllers (2DOF PID and 2DOF FOPID) improved significantly the performance of the ordinary PID controllers.

Editor-in-Chief prof. dr hab. inż. Andrzej Świerniak

**Deputy/ Managing Editor**

Zbigniew Ogonowski, Silesian University of Technology, Gliwice, Poland

**Editorial Advisory Board**

Andrzej Bargiela, University of Nottingham, UK

Roman Barták, Charles University, Prague, Czech Rep.

Jacek Błażewicz, Poznań University of Technology, Poland

Reggie Davidrajuh, University of Stavanger, Norway

Andreas Deutsch, Technische Universität Dresden, Germany

Moritz Diehl, University of Freiburg, Germany

Władysław Findeisen, Warsaw University of Technology, Poland

Marcelo D.Fragoso, LNCC/MCT, Rio de Janeiro, Brasil

Avner Friedman, MBI Ohio State University, Columbus, USA

Alberto Gandolfi, IASI, Rome, Italy

Ryszard Gessing, Silesian University of Technology, Gliwice, Poland

Henryk Górecki, AGH University of Science and Technology, Poland

David Greenhalgh, University of Strathclyde, Glasgow, UK

Mats Gyllenberg, University of Helsinki, Finland

Wassim M. Haddad, Georigia University, Atlanta, USA

Raimo P. Hämäläinen, Aalto University School of Science, Finland

Alberto Isidori, Università di Roma "La Sapienza" Italia

Laszlo Kevicky, Hungarian Academy of Sciences, Hungary

Marek Kimmel, Rice University Houston, USA

Jerzy Klamka, Silesian University of Technology, Gliwice, Poland

Józef Korbicz, University of Zielona Góra, Poland

Irena Lasiecka, University of Virginia, USA

Urszula Ledzewicz, Southern Illinois University at Edwardsville, USA

Magdi S Mahmoud, KFUM, Dahram, Saudi Arabia

Krzysztof Malinowski, Warsaw University of Technology, Poland

Wojciech Mitkowski, AGH University of Science and Technology, Poland

Bozenna Pasik-Duncan, University of Kansas, Lawrence, USA

Ian Postlethwaite, Newcastle University, Newcastle, UK

Eric Rogers, University of Southampton, UK

Heinz Schaettler, Washington University, St Louis, USA

Ryszard Tadeusiewicz, AGH University of Science and Technology, Poland

Jan Węglarz, Poznań University of Technology, Poland

Liu Yungang, Shandong University, PRC

Valery D. Yurkevich, Novosibirsk State Technical University, Russia

Institute of Automatic Control

Silesian University of Technology

Akademicka 16

44-101 Gliwice, Poland

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http://acs.polsl.pl/

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**Zbigniew Ogonowski**

Institute of Automatic Control

Silesian University of Technology

Akademicka 16

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