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

Słowa kluczowe:
multi-robot system
hybrid control

This article presents a hybrid control system for a group of mobile robots. The components of this system are the supervisory controller(s), employing a discrete, event-driven model of
concurrent robot processes, and robot motion controllers, employing a continuous time model with event-switched modes. The missions of the robots are specified by a sequence of to-be
visited points, and the developed methodology ensures in a formal way their correct accomplishment.

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Słowa kluczowe:
stability analysis
residual energy function as Lyapunov function
physicaldynamic systems
coupled engineering systems

In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a
Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze
stability of engineering system, Lyapunov-like energy function, called residual energy function
is used. The residual function may contain, apart from external energies, negative losses as
well. This function includes the sum of potential and kinetic energies, which are special forms
and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative)
of a system described in different forms using tensorial variables. As the Lypunov function,
residual energy function is defined as Hamiltonian energy function plus loss of energies and
then associated weak and strong stability are proved through the first time-derivative of residual
energy function. It is demonstrated how the stability analysis can be performed using the residual
energy functions in different formulations and in generalized motion space when available.
This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator
for autonomous, and a coupled (electromechanical) example for nonautonomous case. In
the nonautonomous case, the stability criteria can not be proven for one type of formulation,
however, it can be proven in the other type formulation.

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Słowa kluczowe:
fixed point arithmetic
MIMO systems
integer digital filters

The designing of transmultiplexer systems relies on determining filters for the transmitter and receiver sides of multicarrier communication system. The perfect reconstruction conditions
lead to the bilinear equations for FIR filter coefficients. Generally there is no way of finding all possible solutions. This paper describes methods of finding a large family of solutions. Particular
attention is devoted to obtaining algorithms useful in fixed-point arithmetic needed to design the integer filters. As a result, the systems perform perfect reconstruction of signals.
Additionally, a simple method is presented to transform any transmultiplexer into an unlimited number of different transmultiplexers. Finally, two examples of integer filters that meet perfect
reconstruction conditions are shown. The first illustrates a FIR filter which does not require multiplications. The frequency properties of filters and signals are discussed for the second
example.

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Słowa kluczowe:
chaos
chaotic systems
hyperjerk systems
hidden attractors
adaptive control
backstepping control
circuit design

A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to
be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses
a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos
control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical
chaotic model of the hyperjerk system with a hidden chaotic attractor.

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Słowa kluczowe:
descriptor
positive
discrete-time
linear
system
Weierstrass-Kronecker decomposition
minimum energy control

The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated
and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure
for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.

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Słowa kluczowe:
motion planning
nonholonomic
endogenous configuration space
homotopy
continuation
earlier destination reaching

The motion planning problem consists in finding a control function which drives the system to a desired point. The motion planning algorithm derived with an endogenous configuration
space approach assumes that the motion takes place in an arbitrary chosen time horizon. This work introduces a modification to the motion planning algorithm which allows to reach the
destination point in time, which is shorter than the assumed time horizon. The algorithm derivation relies on the endogenous configuration space approach and the continuation (homotopy)
method. To achieve the earlier destination reaching a new formulation of the task map and the task Jacobian are introduced. The efficiency of the new algorithm is depicted with simulation
results.

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Słowa kluczowe:
describing function
dither signal
incremental input describing function
limitcycles
signal stabilization
stability boundary

The paper presents a simple, systematic and novel graphical method which uses computer graphics for prediction of limit cycles in two dimensional multivariable nonlinear system having
rectangular hysteresis and backlash type nonlinearities. It also explores the avoidance of such self-sustained oscillations by determining the stability boundary of the system. The stability
boundary is obtained using simple Routh Hurwitz criterion and the incremental input describing function, developed from harmonic balance concept. This may be useful in interconnected
power system which utilizes governor control. If the avoidance of limit cycle or a safer operating zone is not possible, the quenching of such oscillations may be done by using the signal stabilization
technique which is also described. The synchronization boundary is laid down in the forcing signal amplitudes plane using digital simulation. Results of digital simulations illustrate
accuracy of the method for 2×2 systems.

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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

acs@polsl.pl

http://acs.polsl.pl/

Each paper submitted is subject to a review procedure, and the publication decision is based on reviers' comments on the paper. To avoid delay, please prepare the manuscript carefully following the suggestions listed below.

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**References** should be listed alphabetically at the end of the manuscript. They should be numbered in ascending order and the numbers should be inserted in square brackets. References should be organized as follows. First initial(s), surname(s) of the author(s) and title of article or book. Then, for papers: title of periodical or collective work, volume number (year of issue), issue number, and numbers of the first and the last page; for books: publisher's name(s), place and year of issue. Example:

- R. E. Kalman: Mathematical description of linear dynamical system. SIAM J. Control. 1(2), (1963), 152-192.
- F. C. Shweppe: Uncertain dynamic systems. Prentice-Hall, Englewood Cliffs, N.J. 1970.

Please, give full titles of journals; only common words like Journal, Proceedings, Conference, etc. may be abbreviated ( to J., Proc., Conf., ... respectively). References to publications in the body of the manuscript should be indicated by the numbers of the adequate references in square brackets. When the paper is set in TeX the preferable form of preparing references is Bib TeX bib database.

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**Reprints**. 10 reprints of each paper will be provided free of charge.

**Submission of a paper** implies the Author's irrevocable and exclusive authorization of the publisher to collect any sums or considerations for copying or reproduction payable by third parties.

Papers should be sent to:

**Zbigniew Ogonowski**

Institute of Automatic Control

Silesian University of Technology

Akademicka 16

44-101 Gliwice, Poland