Nauki Techniczne

Archives of Control Sciences


Archives of Control Sciences | 2018 | vol. 28 | No 2 |


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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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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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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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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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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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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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



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

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Zbigniew Ogonowski
Institute of Automatic Control
Silesian University of Technology
Akademicka 16
44-101 Gliwice, Poland

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