Journal of the University of Zielona Góra

International Journal of Applied Mathematics and Computer Science

Int.Jnl Appl.Math.Comp.Sci.ONL

<abstract xml:lang="en"><title style='display:none'>Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems</title>Interval arithmetic techniques such as ValEncIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically meaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics.</abstract>

Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems

Institute of Measurement, Control, and Microtechnology, University of Ulm, D-89069 Ulm, Germany

Keywords

<article-title>Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Dynamical Systems</article-title>

<abstract xml:lang="en"><title style='display:none'>Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems</title>Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SmartMobile enhances the existing MSS Mobile with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities of SmartMobile. In particular, we focus on its use of newly developed methods for sensitivity analysis and DAE solving for several practically relevant mechanical systems.</abstract>

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Faculty of Engineering, INKO, University of Duisburg-Essen, D-47048 Duisburg, Germany

<article-title>Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems</article-title>

<abstract xml:lang="en"><title style='display:none'>Interval Analysis for Certified Numerical Solution of Problems in Robotics</title>Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical computer round-off errors are taken into account so that the solutions are guaranteed; (c) it allows one to take into account the uncertainties that are inherent to a physical system. Properties (a) and (c) are of special interest in robotics problems, in which many of the variables are parameters that are measured (i.e., known only up to some bounded errors) while the modeling of the robot is based on parameters that are submitted to uncertainties (e.g., because of manufacturing tolerances). Taking into account these uncertainties is essential for many robotics applications such as medical or space robotics for which safety is a crucial issue. A further inherent property of interval analysis that is of interest for robotics problems is that this approach allows one to deal with the <italic>uncertainties</italic> that are unavoidable in robotics. Although the basic principles of interval analysis are easy to understand and to implement, this approach will be efficient only if the right heuristics are used and if the problem at hand is formulated appropriately. In this paper we will emphasize various robotics problems that have been solved with interval analysis, many of which are currently beyond the reach of other mathematical approaches.</abstract>

Interval Analysis for Certified Numerical Solution of Problems in Robotics

INRIA, 2004 Route des Lucioles, 06902 Sophia-Antipolis, France

<article-title>Interval Analysis for Certified Numerical Solution of Problems in Robotics</article-title>

{"article-title":"Interval Analysis for Certified Numerical Solution of Problems in Robotics"}

<abstract xml:lang="en"><title style='display:none'>Reliable Robust Path Planning with Application to Mobile Robots</title>This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.</abstract>

Reliable Robust Path Planning with Application to Mobile Robots

L2S-CNRS-SUPELEC—Univ. Paris-Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France

<article-title>Reliable Robust Path Planning with Application to Mobile Robots</article-title>

{"article-title":"Reliable Robust Path Planning with Application to Mobile Robots"}

<abstract xml:lang="en"><title style='display:none'>Nonlinear Stabilizing Control of an Uncertain Bioprocess Model</title>In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is designed to stabilize the dynamics towards the maximum methane output flow rate in the presence of coefficient uncertainties. Computer simulations in Maple are reported to illustrate the theoretical results.</abstract>

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria

<article-title>Nonlinear Stabilizing Control of an Uncertain Bioprocess Model</article-title>

{"article-title":"Nonlinear Stabilizing Control of an Uncertain Bioprocess Model"}

<abstract xml:lang="en"><title style='display:none'>Verified Solution Method for Population Epidemiology Models with Uncertainty</title>Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.</abstract>

Verified Solution Method for Population Epidemiology Models with Uncertainty

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

<article-title>Verified Solution Method for Population Epidemiology Models with Uncertainty</article-title>

{"article-title":"Verified Solution Method for Population Epidemiology Models with Uncertainty"}

<abstract xml:lang="en"><title style='display:none'>An Object-Oriented Approach to Simulating Human Gait Motion Based on Motion Tracking</title>Accurate bone motion reconstruction from marker tracking is still an open and challenging issue in biomechanics. Presented in this paper is a novel approach to gait motion reconstruction based on kinematical loops and functional skeleton features extracted from segmented Magnetic Resonance Imaging (MRI) data. The method uses an alternative path for concatenating relative motion starting at the feet and closing at the hip joints. From the evaluation of discrepancies between predicted and geometrically identified functional data, such as hip joint centers, a cost function is generated with which the prediction model can be optimized. The method is based on the object-oriented multibody library MOBILE, which has already been successfully applied to the development of industrial virtual design environments. The approach has been implemented in a general gait visualization environment termed <italic>Mobile Body</italic>.</abstract>

An Object-Oriented Approach to Simulating Human Gait Motion Based on Motion Tracking

Department of Mechanical and Process Engineering, University of Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany

Department of Orthopaedics, Universitätsklinikum Essen, Hufelandstraße 55, 45147 Essen, Germany

<article-title>An Object-Oriented Approach to Simulating Human Gait Motion Based on Motion Tracking</article-title>

<abstract xml:lang="en"><title style='display:none'>Verified Methods for Computing Pareto Sets: General Algorithmic Analysis</title>In many engineering problems, we face multi-objective optimization, with several objective functions <italic>f</italic>1, …, <italic>f</italic><italic>n</italic>. We want to provide the user with the Pareto set—a set of all possible solutions <italic>x</italic> which cannot be improved in all categories (i.e., for which <italic>fj</italic> (<italic>x</italic>') ≥ <italic>f</italic><italic>j</italic>(<italic>x</italic>) for all <italic>j</italic> and <italic>f</italic><italic>j</italic>(<italic>x</italic>') &gt; <italic>f</italic><italic>j</italic>(<italic>x</italic>) for some <italic>j</italic> is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about (verified) algorithmic computability of maxima locations to show that Pareto sets can also be computed.</abstract>

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Department of Differential Equations, Institute of Mathematics, Budapest University of Technology and Economics (BME), Egry József u. 1, 1111 Budapest, Hungary

Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA

<article-title>Verified Methods for Computing Pareto Sets: General Algorithmic Analysis</article-title>

{"article-title":"Verified Methods for Computing Pareto Sets: General Algorithmic Analysis"}

<abstract xml:lang="en"><title style='display:none'>Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties</title>Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.</abstract>

Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties

Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany

<article-title>Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties</article-title>

<abstract xml:lang="en"><title style='display:none'>A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP</title>The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differential-algebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on ValEncIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, ValEncIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of ValEncIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.</abstract>

A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP

<article-title>A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP</article-title>

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Editor-in-Chief <A href="http://staff.uz.zgora.pl/jkorbicz/">Józef Korbicz</A>, University of Zielona Góra, Poland Deputy Editor <A href="http://staff.uz.zgora.pl/ducinski/viewpage.php?page_id=12">Dariusz Uciński</A>, University of Zielona Góra, Poland Associate Editors Harald ASCHEMANN, University of Rostock, Germany Jérôme CIESLAK, University of Bordeaux, France Martin GUGAT, Friedrich-Alexander University of Erlangen-Nuremberg, Germany Marios M. POLYCARPOU, University of Cyprus, Nicosia, Cyprus Silvio SIMANI, University of Ferrara, Italy Jerzy STEFANOWSKI, Poznań University of Technology, Poland Guisheng ZHAI, Shibaura Institute of Technology, Tokyo, Japan Board Members Cherukuri ASWANI KUMAR, VIT University, Vellore, India Czesław BAJER, Polish Academy of Sciences, Warsaw, Poland Andrzej BARTOSZEWICZ, Technical University of Łódź, Poland Miguel BERNAL, Sonora Institute of Technology (ITSON), Obregón, Mexico Kishore BINGI, Vellore Institute of Technology, India Paolo CASTALDI, University of Bologna, Italy Zhaohui CEN, Qatar Enviroment and Energy Research Institute, Ar Rayyan, Qatar Bogusław CYGANEK, AGH University of Science and Technology, Cracow, Poland Stefan DOMEK, West Pomeranian University of Technology in Szczecin, Poland Andrzej DZIELIŃSKI, Warsaw University of Technology, Poland Anna FABIJAŃSKA, Lodz University of Technology, Poland Marcin GORAWSKI, Silesian University of Technology, Gliwice, Poland Michał GROCHOWSKI, Gdańsk University of Technology, Poland Xiao HE, Tsinghua University, Beijing, China Janusz KACPRZYK, Polish Academy of Sciences, Warsaw, Poland Jerzy KLAMKA, Polish Academy of Sciences, Gliwice, Poland Jacek KLUSKA, Rzeszów University of Technology, Poland Joanna KOŁODZIEJ, Cracow University of Technology, Poland Jan M. KOŚCIELNY, Warsaw University of Technology, Poland Zdzisław KOWALCZUK, Gdańsk University of Technology, Poland Adam KRZYZAK, Concordia University, Montreal, Canada Piotr KULCZYCKI, AGH University of Science and Technology, Cracow, Poland Maciej KUSY, Rzeszów University of Technology, Poland Francisco-Ronay LÓPEZ-ESTRADA, Technological Institute of Tuxtla Gutiérrez, Mexico Maciej ŁAWRYŃCZUK, Warsaw University of Technology, Poland Vyacheslav MAKSIMOV, Russian Academy of Sciences, Ekaterinburg, Russia Krzysztof MALINOWSKI, Warsaw University of Technology, Poland Wojciech MITKOWSKI, AGH University of Science and Technology, Cracow, Poland Gang NIU, Tongji University, Shanghai, China Ronald J. PATTON, University of Hull, UK Jimoh O. PEDRO, University of the Witwatersrand, Johannesburg, South Africa Witold PEDRYCZ, University of Alberta, Edmonton, Canada Piotr PORWIK, University of Silesia in Katowice, Poland Vicenç PUIG, Technical University of Catalonia, Barcelona, Spain Jianbin QIU, Harbin Institute of Technology, China Ewaryst RAFAJŁOWICZ, Wrocław University of Technology, Poland Rotislav RAZUMCHIK, Russian Academy of Sciences, Moscow, Russia Leszek RUTKOWSKI, Technical University of Częstochowa, Poland Andrey V. SAVCHENKO, National Research University HSE, Nizhny Novgorod, Russia Piotr SKRZYPCZYŃSKI, Poznań University of Technology, Poland Roman SŁOWIŃSKI, Poznań University of Technology, Poland Florin STOICAN, University POLITEHNICA of Bucharest, Romania Andrzej ŚWIERNIAK, Silesian University of Technology, Gliwice, Poland Zoltán SZABÓ, Hungarian Academy of Sciences, Budapest, Hungary Ryszard TADEUSIEWICZ, AGH University of Science and Technology, Cracow, Poland Didier THEILLIOL, University of Lorraine, Nancy, France Haoping WANG, Nanjing University of Science and Technology, China Marcin WITCZAK, University of Zielona Góra, Poland Baozhen YAO, Dalian University of Technology, China Shen YIN, Harbin Institute of Technology, China Alexey ZHIRABOK, Far Eastern Federal University, Vladivostok, Russia Teresa ZIELIŃSKA, Warsaw University of Technology, Poland Jacek M. ZURADA, University of Louisville, USA Editorial Office Agnieszka Rożewska, University of Zielona Góra, Poland – Manager Agata Wiśniewska-Kubicka, University of Zielona Góra, Poland – Technical Editor Contact AMCS Editorial Office University of Zielona Góra, Institute of Control and Computation Engineering ul. prof. Z. Szafrana 2 65-516 Zielona Góra phone: +48683282506 e-mail: <A href="mailto:amcs@uz.zgora.pl">amcs@uz.zgora.pl</A> website: <A href="http://www.amcs.uz.zgora.pl/">www.amcs.uz.zgora.pl</A> Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland Acknowledgement Electronic publication of Volume 26 (2016, Nos. 1-4) has been financed with the funds of the Polish Ministry of Science and Higher Education for science promoting activities within the agreement no. 904/P-DUN/2016 <A href="http://www.nauka.gov.pl/en/"><IMG alt="" src="https://www.degruyter.com/staticfiles/images/mnisw_opt.jpg"></A>

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<DIV align=left> The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland (Sciendo) and historically with Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences. The journal strives to meet the demand for the presentation of interdisciplinary research in various fields related to control theory, applied mathematics, scientific computing and computer science. In particular, it publishes high quality original research results in the following areas: <UL> <LI>modern control theory and practice, </LI> <LI>artificial intelligence methods and their applications, </LI> <LI>applied mathematics and mathematical optimisation techniques, </LI> <LI>mathematical methods in engineering, computer science, and biology. </LI> </UL> We are primarily interested in presenting theoretical and application-orientated full-length research papers dealing with the following topics: <UL> <LI>control theory, including optimal control, system identification, adaptive and robust control, multivariable control, and non-linear systems, </LI> <LI>dynamical systems, including spatiotemporal processes, control problems, state and parameter estimation, and sensor networks, </LI> <LI>fault detection and diagnosis, including model-based approaches, observers, and classifiers, </LI> <LI>fault-tolerant control, including the control of continuous-variable and quantised systems, </LI> <LI>robotics, including modelling and simulation, mobile robots, and optimal trajectory planning, </LI> <LI>mathematical modelling and simulation, including numerical algorithms, </LI> <LI>optimisation, including mathematical optimisation techniques, global optimisation, and evolutionary algorithms, </LI> <LI>artificial intelligence, including machine and deep learning, neural networks, knowledge engineering, fuzzy systems, and search methods, </LI> <LI>data mining, data and image processing, and big data, </LI> <LI>classification and pattern recognition, </LI> <LI>biomedical engineering and biomathematics, </LI> <LI>applications in engineering and medicine. </LI> </UL> The editors welcome proposals for exchange between similar journals. Also, all persons interested in bringing out special issues or sections of AMCS are encouraged to contact the Editor-in-Chief. Specials may be published on any important and timely subject within the scope of the journal. All papers proposed for special issues or sections will be refereed and have to meet the same criteria for scientific quality as articles presented in regular issues. Also, all journal rules and guidelines refer to papers published in specials without any exceptions. ISSN: 1641-876X (print version), 2083-8492 (online version) Why subscribe and read <UL> <LI>Premier source of high quality research from all over the world, with special emphasis on papers from Central and Eastern Europe, </LI> <LI>over twenty years of experience in publishing original articles dealing with various aspects of applying mathematical methods to computer science and engineering, </LI> <LI>extensive scope covering, among other things, control systems, optimization, robotics, mathematical and numerical modeling, artificial intelligence, knowledge processing, fault detection and diagnostics, </LI> <LI>one of the fastest growing journals published in Central and Eastern Europe. </LI></UL> Why submit <UL> <LI>Fast, fair, competent and comprehensive peer review (two or three referees are designated for the assessment of each manuscript), </LI> <LI>fast and efficient publication process, </LI> <LI>thorough language correction for authors who are not native English speakers, </LI> <LI>polishing the structure and technical format of each submission, </LI> <LI>promotion of published papers in the vast scientific community of researchers working in the field. </LI></UL> Archiving Sciendo archives the contents of this journal in <A href="https://www.portico.org/">Portico</A> - digital long-term preservation service of scholarly books, journals and collections. Plagiarism policy The editorial board is participating in a growing community of <A href="https://www.crossref.org/services/similarity-check/">Similarity Check System's</A> users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. </DIV>

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Volume 19 (2009): Issue 3 (September 2009) Verified Methods: Applications in Medicine and Engineering (special issue), Andreas Rauh, Ekaterina Auer, Eberhard P. Hofer and Wolfram Luther (Eds.)

Volume 19 (2009): Issue 3 (September 2009)

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