We are interested in an efficient solution of optimal control problems of dynamic processes under uncertainty. This comprises the inclusion of risk measures, such as worst case, expected value, Value at Risk, or Conditional Value at Risk into the problem formulation. It also comprises optimal control with stochastic differential equations. We have been developing a novel generic methodology to solve continuous finite-horizon stochastic optimal control problems (SOCPs). We treat controlled stochastic differential equations (SDEs) within the Wiener chaos framework by utilizing Malliavin calculus and developing innovative ideas to preserve the feedback character of optimal Markov decision rules. This allows a direct reformulation of SOCPs into deterministic ones. Hence, it facilitates using Bock's direct multiple shooting method for solving SOCPs and pioneers the extension of sophisticated methods for deterministic control to the broad context of SDEs.
Selected publications
@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}
}
@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}
}
@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}
}
@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}
}
@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 = {https://optimization-online.org/?p=12172}
}
@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}
}
@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}
}