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
| Author | Title | Year | Journal/Proceedings | Reftype | Link |
|---|---|---|---|---|---|
| Huschto, T., Podolskij, M., Sager, S. | The asymptotic error of chaos expansion approximations for stochastic differential equations [BibTeX] |
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}
} |
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| Jost, F., Sager, S., Le, T. | A Feedback Optimal Control Algorithm with Optimal Measurement Time Points [BibTeX] |
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}
} |
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| 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 [BibTeX] |
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}
} |
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| Matke, C., Medjroubi, W., Kleinhans, D., Sager, S. | Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID [BibTeX] |
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}
} |
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| Huschto, T., Sager, S. | Pricing Conspicuous Consumption Products in Recession Periods with Uncertain Strength [BibTeX] |
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}
} |
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| Huschto, T., Sager, S. | Solving Stochastic Optimal Control Problems by a Wiener Chaos Approach [BibTeX] |
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}
} |
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| Huschto, T. | Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations [BibTeX] |
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}
} |
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Further references of the MathOpt group can be found on this page.