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Journal & Issues

Volume 32 (2022): Issue 3 (September 2022)
Recent Advances in Modelling, Analysis and Implementation of Cyber-Physical Systems (Special section, pp. 345-413), Remigiusz Wiśniewski, Luis Gomes and Shaohua Wan (Eds.)

Volume 32 (2022): Issue 2 (June 2022)
Towards Self-Healing Systems through Diagnostics, Fault-Tolerance and Design (Special section, pp. 171-269), Marcin Witczak and Ralf Stetter (Eds.)

Volume 32 (2022): Issue 1 (March 2022)

Volume 31 (2021): Issue 4 (December 2021)
Advanced Machine Learning Techniques in Data Analysis (special section, pp. 549-611), Maciej Kusy, Rafał Scherer, and Adam Krzyżak (Eds.)

Volume 31 (2021): Issue 3 (September 2021)

Volume 31 (2021): Issue 2 (June 2021)

Volume 31 (2021): Issue 1 (March 2021)

Volume 30 (2020): Issue 4 (December 2020)

Volume 30 (2020): Issue 3 (September 2020)
Big Data and Signal Processing (Special section, pp. 399-473), Joanna Kołodziej, Sabri Pllana, Salvatore Vitabile (Eds.)

Volume 30 (2020): Issue 2 (June 2020)

Volume 30 (2020): Issue 1 (March 2020)

Volume 29 (2019): Issue 4 (December 2019)
New Perspectives in Nonlinear and Intelligent Control (In Honor of Alexander P. Kurdyukov) (special section, pp. 629-712), Julio B. Clempner, Enso Ikonen, Alexander P. Kurdyukov (Eds.)

Volume 29 (2019): Issue 3 (September 2019)
Information Technology for Systems Research (special section, pp. 427-515), Piotr Kulczycki, Janusz Kacprzyk, László T. Kóczy, Radko Mesiar (Eds.)

Volume 29 (2019): Issue 2 (June 2019)
Advances in Complex Cloud and Service Oriented Computing (special section, pp. 213-274), Anna Kobusińska, Ching-Hsien Hsu, Kwei-Jay Lin (Eds.)

Volume 29 (2019): Issue 1 (March 2019)
Exploring Complex and Big Data (special section, pp. 7-91), Johann Gamper, Robert Wrembel (Eds.)

Volume 28 (2018): Issue 4 (December 2018)

Volume 28 (2018): Issue 3 (September 2018)

Volume 28 (2018): Issue 2 (June 2018)
Advanced Diagnosis and Fault-Tolerant Control Methods (special section, pp. 233-333), Vicenç Puig, Dominique Sauter, Christophe Aubrun, Horst Schulte (Eds.)

Volume 28 (2018): Issue 1 (March 2018)
Issues in Parameter Identification and Control (special section, pp. 9-122), Abdel Aitouche (Ed.)

Volume 27 (2017): Issue 4 (December 2017)

Volume 27 (2017): Issue 3 (September 2017)
Systems Analysis: Modeling and Control (special section, pp. 457-499), Vyacheslav Maksimov and Boris Mordukhovich (Eds.)

Volume 27 (2017): Issue 2 (June 2017)

Volume 27 (2017): Issue 1 (March 2017)

Volume 26 (2016): Issue 4 (December 2016)

Volume 26 (2016): Issue 3 (September 2016)

Volume 26 (2016): Issue 2 (June 2016)

Volume 26 (2016): Issue 1 (March 2016)

Volume 25 (2015): Issue 4 (December 2015)
Special issue: Complex Problems in High-Performance Computing Systems, Editors: Mauro Iacono, Joanna Kołodziej

Volume 25 (2015): Issue 3 (September 2015)

Volume 25 (2015): Issue 2 (June 2015)

Volume 25 (2015): Issue 1 (March 2015)
Safety, Fault Diagnosis and Fault Tolerant Control in Aerospace Systems, Silvio Simani, Paolo Castaldi (Eds.)

Volume 24 (2014): Issue 4 (December 2014)

Volume 24 (2014): Issue 3 (September 2014)
Modelling and Simulation of High Performance Information Systems (special section, pp. 453-566), Pavel Abaev, Rostislav Razumchik, Joanna Kołodziej (Eds.)

Volume 24 (2014): Issue 2 (June 2014)
Signals and Systems (special section, pp. 233-312), Ryszard Makowski and Jan Zarzycki (Eds.)

Volume 24 (2014): Issue 1 (March 2014)
Selected Problems of Biomedical Engineering (special section, pp. 7 - 63), Marek Kowal and Józef Korbicz (Eds.)

Volume 23 (2013): Issue 4 (December 2013)

Volume 23 (2013): Issue 3 (September 2013)

Volume 23 (2013): Issue 2 (June 2013)

Volume 23 (2013): Issue 1 (March 2013)

Volume 22 (2012): Issue 4 (December 2012)
Hybrid and Ensemble Methods in Machine Learning (special section, pp. 787 - 881), Oscar Cordón and Przemysław Kazienko (Eds.)

Volume 22 (2012): Issue 3 (September 2012)

Volume 22 (2012): Issue 2 (June 2012)
Analysis and Control of Spatiotemporal Dynamic Systems (special section, pp. 245 - 326), Dariusz Uciński and Józef Korbicz (Eds.)

Volume 22 (2012): Issue 1 (March 2012)
Advances in Control and Fault-Tolerant Systems (special issue), Józef Korbicz, Didier Maquin and Didier Theilliol (Eds.)

Volume 21 (2011): Issue 4 (December 2011)

Volume 21 (2011): Issue 3 (September 2011)
Issues in Advanced Control and Diagnosis (special section, pp. 423 - 486), Vicenç Puig and Marcin Witczak (Eds.)

Volume 21 (2011): Issue 2 (June 2011)
Efficient Resource Management for Grid-Enabled Applications (special section, pp. 219 - 306), Joanna Kołodziej and Fatos Xhafa (Eds.)

Volume 21 (2011): Issue 1 (March 2011)
Semantic Knowledge Engineering (special section, pp. 9 - 95), Grzegorz J. Nalepa and Antoni Ligęza (Eds.)

Volume 20 (2010): Issue 4 (December 2010)

Volume 20 (2010): Issue 3 (September 2010)

Volume 20 (2010): Issue 2 (June 2010)

Volume 20 (2010): Issue 1 (March 2010)
Computational Intelligence in Modern Control Systems (special section, pp. 7 - 84), Józef Korbicz and Dariusz Uciński (Eds.)

Volume 19 (2009): Issue 4 (December 2009)
Robot Control Theory (special section, pp. 519 - 588), Cezary Zieliński (Ed.)

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 2 (June 2009)

Volume 19 (2009): Issue 1 (March 2009)

Volume 18 (2008): Issue 4 (December 2008)
Issues in Fault Diagnosis and Fault Tolerant Control (special issue), Józef Korbicz and Dominique Sauter (Eds.)

Volume 18 (2008): Issue 3 (September 2008)
Selected Problems of Computer Science and Control (special issue), Krzysztof Gałkowski, Eric Rogers and Jan Willems (Eds.)

Volume 18 (2008): Issue 2 (June 2008)
Selected Topics in Biological Cybernetics (special section, pp. 117 - 170), Andrzej Kasiński and Filip Ponulak (Eds.)

Volume 18 (2008): Issue 1 (March 2008)
Applied Image Processing (special issue), Anton Kummert and Ewaryst Rafajłowicz (Eds.)

Volume 17 (2007): Issue 4 (December 2007)

Volume 17 (2007): Issue 3 (September 2007)
Scientific Computation for Fluid Mechanics and Hyperbolic Systems (special issue), Jan Sokołowski and Eric Sonnendrücker (Eds.)

Volume 17 (2007): Issue 2 (June 2007)

Volume 17 (2007): Issue 1 (March 2007)

Journal Details
Format
Journal
eISSN
2083-8492
ISSN
1641-876X
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English

Search

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.)

Journal Details
Format
Journal
eISSN
2083-8492
ISSN
1641-876X
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English

Search

10 Articles
Open Access

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Published Online: 24 Sep 2009
Page range: 369 - 380

Abstract

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

In many engineering problems, we face multi-objective optimization, with several objective functions f1, …, fn. We want to provide the user with the Pareto set—a set of all possible solutions x which cannot be improved in all categories (i.e., for which fj (x') ≥ fj(x) for all j and fj(x') > fj(x) for some j 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.

Keywords

  • multi-objective optimization
  • Pareto set
  • verified computing
Open Access

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

Published Online: 24 Sep 2009
Page range: 381 - 397

Abstract

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

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.

Keywords

  • ordinary differential equations
  • differential-algebraic equations
  • ValEncIA-IVP
  • verified simulation
  • inverse control problems
Open Access

Interval Analysis for Certified Numerical Solution of Problems in Robotics

Published Online: 24 Sep 2009
Page range: 399 - 412

Abstract

Interval Analysis for Certified Numerical Solution of Problems in Robotics

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 uncertainties 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.

Keywords

  • interval analysis
  • uncertainties
  • robotics
Open Access

Reliable Robust Path Planning with Application to Mobile Robots

Published Online: 24 Sep 2009
Page range: 413 - 424

Abstract

Reliable Robust Path Planning with Application to Mobile Robots

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.

Keywords

  • interval analysis
  • path planning
  • robust control
  • state-space models
Open Access

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

Published Online: 24 Sep 2009
Page range: 425 - 439

Abstract

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

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.

Keywords

  • interval arithmetic
  • reachability analysis
  • observability analysis
  • robust stability
  • model-based design of optimal controllers
Open Access

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

Published Online: 24 Sep 2009
Page range: 441 - 454

Abstract

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

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.

Keywords

  • wastewater treatment model
  • local bifurcations of steady states
  • asymptotic stabilization
  • extremum seeking
  • uncertain data
Open Access

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

Published Online: 24 Sep 2009
Page range: 455 - 467

Abstract

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

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.

Keywords

  • multibody systems
  • result verification
  • sensitivity
  • DAE
  • uncertainty
Open Access

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

Published Online: 24 Sep 2009
Page range: 469 - 483

Abstract

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

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 Mobile Body.

Keywords

  • gait/motion analysis
  • muskuloskeletal system
  • multibody simulation
  • MRI
  • X-ray
  • motion tracking
Open Access

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

Published Online: 24 Sep 2009
Page range: 485 - 499

Abstract

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

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.

Keywords

  • ValEncIA-IVP
  • consistency tests for the reduction of overestimation
  • identification of dynamical constraints
  • Hamiltonian systems
  • branch and prune algorithms
Open Access

Verified Solution Method for Population Epidemiology Models with Uncertainty

Published Online: 24 Sep 2009
Page range: 501 - 512

Abstract

Verified Solution Method for Population Epidemiology Models with Uncertainty

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.

Keywords

  • nonlinear dynamics
  • epidemiology
  • interval analysis
  • verified computing
  • ordinary differential equations
10 Articles
Open Access

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Published Online: 24 Sep 2009
Page range: 369 - 380

Abstract

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

In many engineering problems, we face multi-objective optimization, with several objective functions f1, …, fn. We want to provide the user with the Pareto set—a set of all possible solutions x which cannot be improved in all categories (i.e., for which fj (x') ≥ fj(x) for all j and fj(x') > fj(x) for some j 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.

Keywords

  • multi-objective optimization
  • Pareto set
  • verified computing
Open Access

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

Published Online: 24 Sep 2009
Page range: 381 - 397

Abstract

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

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.

Keywords

  • ordinary differential equations
  • differential-algebraic equations
  • ValEncIA-IVP
  • verified simulation
  • inverse control problems
Open Access

Interval Analysis for Certified Numerical Solution of Problems in Robotics

Published Online: 24 Sep 2009
Page range: 399 - 412

Abstract

Interval Analysis for Certified Numerical Solution of Problems in Robotics

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 uncertainties 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.

Keywords

  • interval analysis
  • uncertainties
  • robotics
Open Access

Reliable Robust Path Planning with Application to Mobile Robots

Published Online: 24 Sep 2009
Page range: 413 - 424

Abstract

Reliable Robust Path Planning with Application to Mobile Robots

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.

Keywords

  • interval analysis
  • path planning
  • robust control
  • state-space models
Open Access

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

Published Online: 24 Sep 2009
Page range: 425 - 439

Abstract

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

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.

Keywords

  • interval arithmetic
  • reachability analysis
  • observability analysis
  • robust stability
  • model-based design of optimal controllers
Open Access

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

Published Online: 24 Sep 2009
Page range: 441 - 454

Abstract

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

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.

Keywords

  • wastewater treatment model
  • local bifurcations of steady states
  • asymptotic stabilization
  • extremum seeking
  • uncertain data
Open Access

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

Published Online: 24 Sep 2009
Page range: 455 - 467

Abstract

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

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.

Keywords

  • multibody systems
  • result verification
  • sensitivity
  • DAE
  • uncertainty
Open Access

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

Published Online: 24 Sep 2009
Page range: 469 - 483

Abstract

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

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 Mobile Body.

Keywords

  • gait/motion analysis
  • muskuloskeletal system
  • multibody simulation
  • MRI
  • X-ray
  • motion tracking
Open Access

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

Published Online: 24 Sep 2009
Page range: 485 - 499

Abstract

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

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.

Keywords

  • ValEncIA-IVP
  • consistency tests for the reduction of overestimation
  • identification of dynamical constraints
  • Hamiltonian systems
  • branch and prune algorithms
Open Access

Verified Solution Method for Population Epidemiology Models with Uncertainty

Published Online: 24 Sep 2009
Page range: 501 - 512

Abstract

Verified Solution Method for Population Epidemiology Models with Uncertainty

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.

Keywords

  • nonlinear dynamics
  • epidemiology
  • interval analysis
  • verified computing
  • ordinary differential equations

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