Mobility

Triggered by technological advances, automated driving of vehicles is a reality. Actually driving vehicles, the use of integrated training devices that tell drivers what they should do, and GPS based look-ahead control strategies raise the question of what the optimal way of driving the vehicle would be. Optimality typically refers to energy consumption, time, driver's comfort, hardware wear-off, or a combination of these objectives.

Control problems that arise in this research field have at least two characteristics which stimulate development of novel mathematical methods. First, the real-time requirements are high as the time between measurements and a reaction of the controler is limited due to the possibly high driving speed. Second, models of interest involve discrete decisions, such as the optimal choice of gear or mode of operation in hybrid vehicles. Or switching behavior of traffic lights. Nonlinear Model Predictive Control problems in Automotive Engineering are hence in the class of MIOCP.

This YouTube video is an exemplary visualization of a time-optimal ride on the Hockenheim ring, by Florian Kehrle and Sebastian Sager. The solution has been calculated with modern mathematical methods. It is based on a simplified dynamical model, including nonlinear tire dynamics. The optimization took the gear choice explicitely into account. The solution is open loop without any feedback and for one complete round.

Selected publications



AuthorTitleYearJournal/ProceedingsReftypeLink
Huschto, T., Podolskij, M., Sager, S. The asymptotic error of chaos expansion approximations for stochastic differential equations 2019 Modern Stochastics: Theory and Applications   article DOI
 
BibTeX:
@article{Huschto2019,
    author = {Huschto, T. and Podolskij, M. and Sager, S.},
    title = {The asymptotic error of chaos expansion approximations for stochastic differential equations},
    journal = {Modern {S}tochastics: {T}heory and {A}pplications},
    year = {2019},
    volume = {6},
    number = {2},
    pages = {145--165},
    doi = {10.15559/19-VMSTA133}
}
Jost, F., Sager, S., Le, T. A Feedback Optimal Control Algorithm with Optimal Measurement Time Points 2017 Processes   article
url  
BibTeX:
@article{Jost2017,
    author = {Jost, F. and Sager, S. and Le, T.T.T.},
    title = {A Feedback Optimal Control Algorithm with Optimal Measurement Time Points},
    journal = {Processes},
    year = {2017},
    volume = {5},
    number = {10},
    pages = {1--19},
    url = {http://www.mdpi.com/2227-9717/5/1/10}
}
Matke, C., Bienstock, D., Munoz, G., Yang, S., Kleinhans, D., Sager, S. Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies 2017 Studies in Computational Intelligence: Complex Networks and Their Applications V   inproceedings DOI
 
BibTeX:
@inproceedings{Matke2017,
    author = {Matke, C. and Bienstock, D. and Munoz, G. and Yang, S. and Kleinhans, D. and Sager, S.},
    title = {Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies},
    booktitle = {Studies in Computational Intelligence: Complex Networks and Their Applications V},
    year = {2017},
    number = {693},
    pages = {809--820},
    doi = {10.1007/978-3-319-50901-3}
}
Matke, C., Medjroubi, W., Kleinhans, D., Sager, S. Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID 2017 Advances in Energy System Optimization   inproceedings
 
BibTeX:
@inproceedings{Matke2017a,
    author = {Matke, Carsten and Medjroubi, Wided and Kleinhans, David and Sager, Sebastian},
    title = {Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID},
    booktitle = {Advances in Energy System Optimization},
    publisher = {Springer International Publishing},
    year = {2017},
    editor = {Bertsch, Valentin and Fichtner, Wolf and Heuveline, Vincent and Leibfried, Thomas},
    pages = {177--188},
    address = {Cham}
}
Huschto, T., Sager, S. Pricing Conspicuous Consumption Products in Recession Periods with Uncertain Strength 2014 European Journal of Decision Processes   article
url  
BibTeX:
@article{Huschto2014,
    author = {Huschto, T. and Sager, S.},
    title = {{P}ricing {C}onspicuous {C}onsumption {P}roducts in {R}ecession {P}eriods with {U}ncertain {S}trength},
    journal = {{E}uropean {J}ournal of {D}ecision {P}rocesses},
    year = {2014},
    volume = {2},
    number = {1--2},
    pages = {3--30},
    url = {http://www.optimization-online.org/DB_HTML/2012/09/3620.html}
}
Huschto, T., Sager, S. Solving Stochastic Optimal Control Problems by a Wiener Chaos Approach 2014 Vietnam Journal of Mathematics   article
url  
BibTeX:
@article{Huschto2014a,
    author = {Huschto, T. and Sager, S.},
    title = {{S}olving {S}tochastic {O}ptimal {C}ontrol {P}roblems by a {W}iener {C}haos {A}pproach},
    journal = {{V}ietnam {J}ournal of {M}athematics},
    year = {2014},
    volume = {42},
    number = {1},
    pages = {83--113},
    url = {https://mathopt.de/publications/Huschto2014a.pdf}
}
Huschto, T. Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations 2014 School: University Heidelberg   phdthesis
url  
BibTeX:
@phdthesis{Huschto2014b,
    author = {Huschto, T.},
    title = {{N}umerical {M}ethods for {R}andom {P}arameter {O}ptimal {C}ontrol and the {O}ptimal {C}ontrol of {S}tochastic {D}ifferential {E}quations},
    school = {University Heidelberg},
    year = {2014},
    url = {https://mathopt.de/publications/Huschto2014.pdf}
}

Further references of the MathOpt group can be found on this page.

  • currently no upcoming news

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Prof. Dr. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto-von-Guericke University Magdeburg

Universitätsplatz 2, 02-224
39106 Magdeburg, Germany

: +49 391 67 58745
:

Susanne Heß

Universitätsplatz 2, 02-201
39106 Magdeburg, Germany

: +49 391 67 58756
:

  • currently no upcoming news

...more

Prof. Dr. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto-von-Guericke University Magdeburg

Universitätsplatz 2, 02-224
39106 Magdeburg, Germany

: +49 391 67 58745
:

Susanne Heß

Universitätsplatz 2, 02-201
39106 Magdeburg, Germany

: +49 391 67 58756
: