Research Projects

Present Research Projects

Fixed-order controller design for linear infinite-dimensional and parameter-varying systems, optimizing stability and H-2 / H-infinity criteria

• Supervisors: W. Michiels, G. Pipeleers, J. Swevers
• Collaborators: J. Peeters
• Duration: 1/1/2011 - 31/12/2014
• Funded by: Fund for Scientific Research-Flanders (FWO-Vlaanderen)
• Project summary:
  The objective of this project is to advance the state of the art in control design methodologies in order to reconcile them with the needs from industry. These needs are fourfold, demanding controller designs that can cope with (i) linear parameter-varying (LPV) systems, as they naturally arise when modeling mechatronic systems such as wafer stages, pick-and-place robots, etc.; (ii) infinite-dimensional dynamics, as most of these systems feature an inherent spatiotemporal distribution of state variables; (iii) model uncertainty; and (iv) a fixed controller structure.
  Currently, no controller design approach addresses all these demands. Current Lyapunov-based approaches apply to LPV systems, but they can only handle limited system order and fail on (iii) and (iv). Current eigenvalue-based approaches, on the other hand, are suited for designing fixed-structured controllers for high-dimensional systems, but they cannot cope with LPV dynamics and fail on (iii). In this project, we will develop methodologies that meet all four demands. The two participating teams each have expertise on either the Lyapunov-based or the eigenvalue-based approaches, and by joining our complementary knowledge we will extend and combine both approaches to cope with the missing demands.

Modeling and simulation of power electronic systems in the complementarity systems framework

• Supervisors: J. Driesen, W. Michiels
• Duration: 1/1/2011 - 31/12/2014
• Funded by: Fund for Scientific Research-Flanders (FWO-Vlaanderen)
• Project summary:
  Power electronics are widely present in applications where one form of electrical energy is converted into another. Example applications include the power supplies in consumer electronics, industrial electric motor drives, electro-heating, lighting and energy-efficient interfaces between renewable energy resources and the distribution grid.
  Power electronic converters make use of semiconductor components operating at a high switching frequency to reach desired dynamics at a slower time scale. Modeling and simulation methods are indispensable for the design and analysis of these converters. Because of the large difference in time scales, non-smooth methods are needed to make a simulation possible in a reasonable amount of time.
  In this project, power electronic systems will be modeled by complementarity systems, a subclass of hybrid systems. A transparent and general framework will be developed, which allows to model complete systems including power electronic circuits, controllers and dynamic loads. At the same time generic numerical methods will be developed for complementarity systems, whose scope reaches far beyond power electronics applications. Finally the project will focus on the simulation of power electronic systems, based on the advantages of the complementarity modeling framework and the developed numerical algorithms.

Center of Excellence: Optimization in Engineering

• Supervisors: M. Diehl (ESAT), J. Vandewalle (ESAT), J. Suykens (ESAT), J. Swevers (MECH), J. De Schutter (MECH), J. Meyers (MECH), J. Van Impe (CIT), I. Smets (CIT), S. Vandewalle (CS), W. Michiels (CS), G. Degrande (BOKU), G. Lombaert (BOKU)
• Collaborators: The whole research division Numerieke Analyse en Toegepaste Wiskunde (NATW)
• Duration: 01/11/2010 - 31/10/2013
• Funded by: Research Council, K.U. Leuven
• Website: OPTEC website
• Project summary:
  The Optimization in Engineering Center (OPTEC) was created in 2005 as one of the twelve Centers of Excellence at the Katholieke Universiteit Leuven. OPTEC is a center of interdisciplinary research on engineering applications of mathematical optimization, emerging from four different engineering fields: computer science, as well as chemical, mechanical and electrical engineering. The main OPTEC objective is to shift the international state of the art by developing new and efficient formulations of the application-specific optimization problems that arise in each of the considered domains. Such new formulations will be the result of synergetic cooperation between top experts in both mathematical programming and each of the application domains, who are brought together within the OPTEC framework.

ExaScience Lab

• Supervisors (local): D. Roose
• Collaborators: All CS members, Ghent University, Free University Brussels, University of Antwerp, Hasselt University, Imec, Flemish Government
• Duration: 01/10/2010 -
• Funded by: IWT, Intel
• Website: ExaScience website
• Project summary:
  The ExaScience Lab develops software for High Performance Computing or HPC. This software will run on future exascale computer systems, delivering 1,000 times the performance of today's fastest supercomputers. The lab is a unique collaboration between Imec, Intel and five Flemish universities.
  Breakthroughs in exascale computing could mean the ability to simulate very complex systems, impossible to replicate today like the human body or Earth's climate. The result, if the computing industry is successful, could mean finding cures for diseases or better predicting natural disasters. The Flanders ExaScience Lab will be focused at enabling scientific applications, beginning with the simulation and prediction of space weather or electromagnetic activity in the space surrounding Earth's atmosphere.

An optimized hierarchical multiscale model for the simulation of plastic deformation of polycrystalline materials

• Supervisors: D. Roose, P. Van Houtte, G. Samaey, A. Van Bael and D. Debruyne
• Collaborators: Jerzy Gawad
• Duration: 1/1/2010 - 31/12/2013
• Funded by: Research Council K.U. Leuven (IDO)
• Project summary (Dutch):
  

  Deze IDO beoogt de ontwikkeling van numerieke methoden en de bijhorende software, om grootschalige vervormingsberekeningen uit te voeren voor metallische materialen op de ingenieursschaal, waarbij gebruik gemaakt wordt van een geoptimaliseerd hiërarchisch meerschalenmodel, met adaptieve actualisering van het constitutief model. Voor de validatie van dit meerschalenmodel worden enerzijds uitgebreide experimenten uitgevoerd met full-field rekmetingen op complexe proefstukken. Anderzijds wordt ook de vergelijking gemaakt qua efficiëntie en nauwkeurigheid met eenvoudige constitutieve modellen die gangbaar zijn in de industrie. De numerieke methoden en de software worden ontworpen met aandacht voor flexibiliteit (voor integratie van andere materiaalmodellen) zodat resultaten van het project ook bruikbaar zullen zijn voor andere toepassingen.

Control and optimization of large-scale systems and networks with delays

• Supervisor: W. Michiels
• Collaborators: J. Vanbiervliet, E. Jarlebring, S. Gumussoy, Z. Wu
• Duration: 1/10/2009 - 30/9/2013
• Funded by: Research Council K.U. Leuven (STRT1/09/31)
• Project summary:
  The aim of the project is to study the effects of time-delays in large-scale dynamical control systems, with the emphasis on systems interconnected in networks. The objectives are:
  
  1. to develop mathematical methods, efficient computational tools and software for analyzing large-scale systems with delays and solving fixed structure controller synthesis problems, within an eigenvalue optimization framework. The synthesis problems concern the stabilization problem, partial pole placement, the optimization of robustness measures in a H2-H-infinity setting, and the optimization of performance measures. The methodology relies on a cross-fertilization of tools from control theory, numerical linear algebra, numerical bifurcation analysis and optimization. It is not perturbation based and exploits structure at various levels;
  
  2. to perform a qualitative analysis of the effect of time-delays in large-scale control systems and networks, in order to reveal the underlying mechanisms. Particular attention will be paid to the influence of the network structure and topology, in relation with the local dynamics, on the overall behavior of the system, and to the generality and scalability of the results. Appropriate controller structures for classes of systems and networks with delays will be selected accordingly, whose parameters will be tuned using the methods developed in the first part of the project.
  
  These results and tools will be applied to problems ranging from the design of decentralized controllers for multi-agent systems, over the (partial) synchronization of chaotic regimes, to problems from vibration control.

Computational aspects of uncertainty propagation in large and multiscale systems

• Supervisors: S. Vandewalle, D. Roose, G. Samaey
• Collaborators: K. Debrabant, E. Rosseel, S. Corveleyn, K. Delaere
• Duration: 1/10/2009 - 30/9/2013
• Funded by: Research Council K.U. Leuven (OT/09/27)
• Project summary:
  This project aims at the development of numerical algorithms that allow to quantify and control the propagation of parameter uncertainties in mathematical models. We investigate the computational aspects of uncertainty propagation in multiscale models, where the stochasticity of the fine-scale model affects the coarse model and its solution. We examine how to reduce the resulting errors at the coarse scale, and how to match them with spatial and temporal discretization errors. For partial differential equations with uncertain coefficients, we explore new approaches towards the development and analysis of fast and robust iterative solution procedures.

Numerical Simulation of Highly Oscillatory Problems with Applications

• Supervisors: S. Vandewalle, D. Huybrechs
• Duration: 1/1/2010 - 31/12/2013
• Funded by: Fund for Scientific Research-Flanders (FWO-Vlaanderen)
• Project summary:
  The research project aspires a new approach for the numerical simulation of physical processes and models that exhibit wave characteristics. The research consists of three major components. In the first component we study novel methods for the computation of highly oscillatory integrals. The second component deals with the development of novel algorithms for the solution of integral equations that model high frequency wave phenomena. In the third component of the project the new methods and models are applied to solve a number of specific technical and scientific problems.

Fuzzy finite element method (Vaagheidsgevoelige eindige-elementenmethode)

• Supervisors: S. Vandewalle, D. Vandepitte (PMA, K.U.Leuven), G. De Roeck (BWK, K.U.Leuven), E. Kerre (U.Gent), G. De Cooman (U.Gent), H. Van der Auweraer (LMS), J.-P. Rammant (SCIA), J. Van Dyck (Probabilitas)
• Collaborators: Eveline Rosseel, Sam Corveleyn, Venkata Rama Rao Mallela, Koen Delaere
• Duration: 1/11/2007 - 31/8/2012
• Funded by: IWT (SBO-060043)
• Partners: K.U.Leuven: PMA Division, Structural Mechanics, Scientific Computing group U.Gent, Fuzziness and Uncertainty Modelling, SYSTemS research group Industrial: LMS International N.V., SCIA GROUP N.V., Probabilitas N.V.
• Project summary:
  The project aims to develop a consistent non-probabilistic finite element approach with a high degree of applicability in numerical analysis in early stages of product development. Next to the development of the numerical methodology, the project also aims at a clear and comprehensive identification and analysis of the application fields of non-probabilistic analysis in typical numerical procedures used for design purposes.

DYSCO: Dynamical Systems, Control and Optimization (2007 - 2011)

• Supervisors: D. Roose, M. Gevers (UCL), J. Vandewalle (K.U.Leuven), D. Aeyels (U.Gent), R. Pintelon (VUB), R. Sépulchre (U.Liège), M. Kinnaert (ULB), A. Vande Wouwer (FPMs)
• Collaborators: the whole research group
• Duration: 01/01/2007 - 31/12/2011
• Funded by: Belgian Federal Science Policy Office (IUAP programme - Interuniversity Attraction Poles)
• Partners:CESAME, U.C.L.; ESAT-SISTA, K.U.Leuven; Systems, University of Gent; Dept. Electrotechniek, VUB; Systèmes, U.Liège; SAAS, ULB; Autom, FPMs
• Website: DYSCO website
• Project summary:
  The major goals of this IUAP (Interuniversity Pole of Attraction) are
  1. to promote scientific research in the area of modelling, identification, simulation, control and optimization of complex dynamical systems, that have a wide range of application areas, including physical, chemical, biological and industrial processes.
  2. to educate researchers in high technology through graduate courses, seminars, and joint workshops.
  Particular topics are:
  • multiscale modeling and simulation
  • bifurcation analysis of dynamical systems
  • control of distributed parameter systems (partial differential equations)
  • optimization techniques for large scale systems.

Recently Finished Research Projects

Multi-scale Mechanics of Fruit Tissue

• Supervisors: Herman Ramon (MeBioS), Josse De Baerdemaker (MeBioS), Dirk Roose, Martine Wevers (MTM)
• Collaborators: Pieter Ghysels
• Duration: 1/10/2006 -
• Funded by: Research Council K.U.Leuven and FWO
• Partners: Bioscience Engineering, MeBioS, K.U.Leuven; Materials Performance and Non-destructive Evaluation research group, MTM, K.U.Leuven
• Project summary:
  Texture and damage susceptibility are two important quality attributes of fruit. Both properties of fruit are determined by their mechanical properties. Mathematical models based on continuum mechanics are often used to predict the relationship between the applied loads and the strain or failure of the fruit. However, fruit is a hierarchically structured material, consisting of different types of tissue, each of which is a highly structured arrangement of cells. Furthermore, the cells themselves consist of different materials which also are structured. The relationship between the macroscopic, or apparent, mechanical properties as applied in a continuum model, and this hierarchical structure is not well understood today.
  The project aims at unraveling this relationship by developing a multiscale model for the mechanics of fruit tissue. This multiscale model will integrate mechanical models at the micro-scale (cellular structure) and macro-scale (tissue level, whole fruit). In the multiscale model, evaluation of the (unknown) macroscopic mechanical constitutive relation is replaced by "on the fly" micro simulations in small domains called representative volume elements (RVEs). The overall macroscopic mechanical behavior is thus never explicitly modeled, but instead, it is determined directly from the underlying micro-model, hence capturing the overall macroscopic mechanical behavior in a quantitative way.
  Experimental work to estimate the necessary parameters and validation will be carried out at all scales considered. In a later stage, the influence of various uncertainties (e.g. material parameters, geometry) in the micro-scale model on the overall macroscopic response will be investigated numerically.

Center of Excellence: Optimization in Engineering

• Supervisors: J. Vandewalle (ESAT-SCD), J. Swevers (Mech-PMA), J. Van Impe (CIT-BioTec), S. Vandewalle (CS-NATW)
• Collaborators: the whole research division Numerieke Analyse en Toegepaste Wiskunde (NATW)
• Duration: 01/11/2005 - 31/10/2010
• Funded by: Research Council, K.U. Leuven
• Website: OPTEC website
• Project summary:
  The K.U.Leuven Center of Excellence in Optimization in Engineering is an interdepartemental platform of the Faculty of Engineering that brings together top expertise in optimization, numerical linear algebra, algorithm development, and applications (in electrical, mechanica and chemical engineering) from four K.U.Leuven partners. The research in the Center focusses on the following topics, which have been organized in 5 work packages.
  
  1. Conceptual and theoretical challenges: research on fundamental questions in optimization theory, in support of the other work packages that are more algorithm and application oriented.
  2. System identification and approximation: development of generic methods to obtain mathematical models of measured data. The resulting models can be used for example in engineering designs and in control systems.
  3. Control system design: study of optimization methods for optimal distributed control of noise and vibrations and of tubular reactors; robust controllers for linear parameter varying (LPV) mechatronic systems; optimal adaptive control and model based predictive control (MPC) of (bio)chemical (stirred and tubular) reactors.
  4. Design optimization: research on optimal design of products and systems. In particular the focus is on two applications: optimal design of tubular chemical reactors and dynamic balancing of machines. Other applications in various engineering disciplines are worked out in collaboration with peripheral partners.
  5. Numerical algorithms and software: efficient and robust numerical algorithms are developed, analyzed and implemented for complex and large-scale optimization.

Advanced Numerical Methods for Mathematical Modelling

• Supervisors: R. Cools (NINES, K.U.Leuven)
• Collaborators: the whole research group
• Duration: 1/1/2006 - 31/12/2010
• Funded by: FWO
• Website: Advanced Numerical Methods for Mathematical Modelling website
• Project summary:
  The section "Numerical Analysis and Applied Mathematics" of the Department of Computer Science, to which the research group Scientific Computing belongs, coordinates this FWO Scientific Research Network (WOG). The network consists of 12 research groups active in the field of numerical analysis and the application of numerical methods: 6 Flemish research groups, 2 groups from French-speaking universities, and 4 groups from abroad. Within the section "Numerical Analysis and Applied Mathematics" research focuses on numerical methods and software for quadrature and cubature; differential equations; nonlinear dynamical systems; numerical linear algebra; approximation theory; splines and applications.

Multi-disciplinary Research on the Solar Drivers of Space Weather

• Supervisors: M. Goossens (CPA, K.U.Leuven), S, Poedts (CPA, K.U.Leuven), S. Vandewalle, H. Deconinck (VKI, Brussels)
• Collaborators: Pieter De Ceuninck, Dries Kimpe
• Duration: 1/1/2004 - 31/12/2008
• Funded by:Research Council K.U.Leuven
• Partner:Center for Plasma Astrophysics, K.U.Leuven
• Project summary:
  In recent years it has become more and more clear that perturbations of the magnetic environment of the Earth or the `Space Weather' can have an important influence on telecommunications and space-borne and ground-based technological systems. The drivers of Space Weather perturbations are of solar origin, namely transient phenomena -- of which coronal mass ejections (CMEs) are the most prominent -- superposed on the background solar wind. The purpose of the present project is to study the physics behind the recurrent structure, heating and acceleration of the solar wind, the acceleration of energetic particles, and the formation and propagation of transients like CMEs and induced shocks from their birth in the solar corona up to their arrival at the Earth's magnetosphere. These aspects of Space Weather will be studied theoretically by various means, including global numerical simulations using the three-dimensional magnetohydrodynamics (MHD) equations on massively parallel computers, and observationally by means of thorough analysis and interpretation of a wide range of observational data gathered by ground observations and satellites, including SOHO, ULYSSES, ACE and Cluster II. The predictive capabilities of such global MHD simulation models will be evaluated and discrepancies will be identified.

Numerical Simulation and Analysis of the Macroscopic Dynamics of Microscopic and Stochastic Evolution Laws

• Supervisors: D. Roose, S. Vandewalle, K. Lust
• Collaborators: Kurt Lust, Giovanni Samaey, Bert Seynaeve, Pieter Van Leemput, Christophe Vandekerckhove
• Duration: 1/10/2003 - 30/9/2007
• Funded by: Research Council K.U.Leuven
• Project summary:
  Physical systems can exhibit deterministic macroscopic behaviour, while the underlying processes at the microscopic level are heterogeneous and/or stochastic. For such multiscale phenomena, one can consider partial differential equations (PDEs) with parameters and coefficients in the form of distribution functions. In other cases, only a microscopic evolution law is known. The aim of this project is to develop numerical methods that account for the underlying microscopic processes. We will develop
  • algorithms that enable a numerical simulation of the macroscopic behaviour induced by a microscopic evolution law, in cases where no macroscopic PDE-model is available;
  • methods for the macroscopic-level bifurcation analysis of microscopic evolution laws, without ever using an explicit macroscopic model;
  • fast solvers for the analysis of the propagation of the parameter uncertainties of a PDE with parameters and coefficients given in the form of distribution functions.

Predictive tools for permeability, mechanical and electro-magnetic properties of fibrous assemblies: Modelling, simulations and experimental verification

• Supervisors: D. Roose, I. Verpoest (MTM), S. Lomov (MTM), G. Vandenbosch (ESAT/TELEMIC), H. Sol (VUB)
• Collaborators: Bart Verleye
• Duration: 1/6/2003 - 31/5/2007
• Funded by: IWT (GBOU)
• Partners: Composites and ceramics, MTM, K.U.Leuven; ESAT/TELEMIC, K.U.Leuven; Mechanics of Materials and Constructions, VUB
• Project summary:
  Fibrous assemblies (textile fabrics or random mats) can be considered as a porous medium. An important parameter characterising the properties of the fibrous material is the permeability tensor. Darcy's law gives the relation between the permeability, the fluid flux, the kinematic viscosity and the pressure of the fluid. In this project we will solve the Navier-Stokes (N-S) and the Brinkmann equations numerically to compute the flow field, and then determine the permeability tensor. We will solve the partial differential equations using a finite difference discretisation on a staggered grid. In case of permeable yarns, the cells of the mesh are divided into N-S cells and Brinkman cells, in which respectively the Navier-Stokes and the Brinkman equations are solved. Since the Brinkmann equations can be seen as the N-S equations with an extra term (depending on the local permeability of the tow), we can combine both models to one system of the PDE with discontinuous coefficients. The underlying models and the software will be validated via experimental data.

Dynamical Systems and Control: Computation, Identification and Modelling

• Supervisors: D. Roose, M. Gevers (UCL), B. De Moor (ESAT/SISTA, K.U.Leuven), D. Aeyels (U.Gent), R. Pintelon (VUB), R. Sépulchre (U.Liège), J. Van Impe (BioTeC, K.U.Leuven)
• Collaborators: the whole research group
• Duration: 01/01/2002 - 31/12/2006
• Funded by: Belgian Federal Science Policy Office (IUAP programme -Interuniversity Attraction Pole)
• Partners: CESAME, U.C.L.; ESAT-SISTA, K.U.Leuven; Systems, University of Gent; Dept. Electrotechniek, VUB; Systèmes, U.Liège; BioTeC, K.U.Leuven
• Website: DYSCO website
• Project summary:
  The major goals of this IUAP (Interuniversity Pole of Attraction) is
  1. to promote scientific research in the area of modelling, identification, simulation and control of complex dynamical systems, that have a wide range of application areas, including virtually all industrial and production processes.
  2. to educate researchers in high technology through graduate courses, seminars, and joint workshops.
  Particular topics are:
  • control of systems with time-delay
  • control of distributed parameter systems (partial differential equations)
  • bifurcation analysis of delay and neutral functional differential equations
  • analysis of periodic solutions in large-scale dynamical systems described by partial differential equations.

Fast solvers and model reduction techniques for 3-dimensional electromagnetic systems

• Supervisors: S. Vandewalle, K. Hameyer (ESAT/ELECTA), F. Henrotte (ESAT/ELECTA)
• Collaborators: Tim Boonen, Geoffrey Deliège
• Duration: 1/1/2003 - 31/12/2006
• Funded by: FWO
• Partners: ESAT/ELECTA, K.U.Leuven
• Project summary:
  The first part of this project aims at the development of fast solvers for 3D edge-element based finite element models of electromechanical devices. Geometric and algebraic multilevel methods are considered in particular, for the 3D Maxwell equations in curl-curl formulation. Based on accurate finite element simulations of the PDEs that model the devices, low dimensional but accurate linear or non-linear ODE-models will be constructed in the second part of the project, by using specialized PDE model reduction techniques. Those ODE-models will then replace the PDE-models in coupled simulations. The model reduction enables the use of efficient, robust, readily available and well-known software tools for the simulation, control and analysis of the entire system.

Numerical Stability and Bifurcation Analysis of Integral Equations with Delay and Microscopic Evolution Laws

• Supervisors: D. Roose, S. Vandewalle, K. Lust
• Collaborators: Kurt Lust, Tatyana Luzyanina, Pieter Van Leemput, Koen Verheyden
• Duration: 1/1/2003 - 31/12/2006
• Funded by: FWO
• Project summary:
  Mathematical models for time evolution can be formulated as integral equations, such as Volterra equations, or microscopic evolution laws, such as cellular automata and lattice-Boltzmann models. Such models are of increasing importance in some areas of physics and mathematical biology. However, numerical methods for simulation (time integration), stability analysis and bifurcation analysis of such models are not well developed yet. In this project, we use our expertise in numerical methods for delay and partial differential equations to develop numerical methods for the stability and bifurcation analysis of a) delay integral equations (DIE) and b) lattice-Boltzmann models (LBM) and cellular automata (CA). These methods will be used in other projects, where we collaborate with groups dealing with applications in population dynamics and fluid dynamics.

Computational Mathematics in Bio-processes

• Supervisors: D. Roose, S. Vandewalle, J. Van Impe (BioTeC, K.U.Leuven), B. Nicolaï (Lab. For Postharvest Techn., K.U.Leuven)
• Collaborators: Koen Engelborghs, Kurt Lust, Tatyana Luzyanina, Giovanni Samaey, Bert Seynaeve, Dominik Smits, Christophe Vandekerckhove, Tatiana Voitovich
• Duration: 01/10/2001 - 30/09/2003
• Funded by: BOF K.U.Leuven
• Partners: BioTeC (K.U.Leuven) and Lab. for Postharvest Technology (K.U.Leuven)
• Project summary:
  A research team with experimental and mathematical experience in biological process engineering and a team with experience in mathematical and numerical techniques will collabroate on fundamental issues in Computational Mathematics in Bioprocesses. Research topics are: numerical methods for delay differential equations and partial differential equations, single species and multiple species microbial evolution, modeling of postharvest storage of fruits, modeling and control of complex (bio-)reactors.