Multiscale Control Concepts for Transport-Dominated Problems

Description

In recent years, the description of controllable (or active) particle systems using methods of kinetic gas theory has been achieved and allows now to tackle a wide range of applications as for example traffic flow. In this research project, the inherent hierarchy exploited extensively in kinetic theory for theoretical and numerical considerations will be investigated in order to develop novel analytical and numerical methods for control problems posed on multiple scales as well as under aspects of non-smoothness in the control. The work program includes the analysis of consistent optimality conditions within the model hierarchies, numerical analysis for control aspects relevant in particular on the highest level of the model hierarchy, as well as the development of numerical methods for time-dynamic non-smooth optimization problems on all levels. In addition to the sensitivity of non-smooth kinetic equations, the multi-scale nature of the equations raises questions for boundary control problems of nonlocal hyperbolic equations and switching systems.

Publications

No publications from this project yet.

Preprints

Martin Frank, Michael Herty, Torsten Trimborn: Microscopic Derivation of Mean Field Game Models (SPP1962-126, 11/2019, [bib])

Research Area

Modeling, problem analysis, algorithm design and convergence analysis

The focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.

Realization of algorithms, adaptive discretization and model reduction

As the target applications of this SPP involve non-smooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper model-reduction techniques need to be developed.

Members

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    Prof. Mapundi Banda

    University of Pretoria
    Principal Investigator
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    Prof. Simone Göttlich

    Universität Mannheim
    Principal Investigator
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    Prof. Michael Herty

    RWTH Aachen
    Principal Investigator
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    Anna Thünen

    RWTH Aachen
    Research Assistant
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    Gediyon Weldegiyorgis

    University of Pretoria
    Research Assistant
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    Dr. Sonja Steffensen

    RWTH Aachen
    Cooperation Partner

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