%0 Journal Article %1 Schmidt2018f %A Schmidt, A. %A Haasdonk, Bernard %D 2018 %J IFAC-PapersOnLine %K Kernel anm approximation, control, dynamic feedback greedy ians optimal principle, programming techniques %N 2 %P 307--312 %R https://doi.org/10.1016/j.ifacol.2018.03.053 %T Data-driven surrogates of value functions and applications to feedback control for dynamical systems %U http://www.sciencedirect.com/science/article/pii/S2405896318300570 %V 51 %X Dealing with high-dimensional feedback control problems is a difficult task when the classical dynamic programming principle is applied. Existing techniques restrict the application to relatively low dimensions since the discretizations typically suffer from the curse of dimensionality. In this paper we introduce a novel approximation technique for the value function of an infinite horizon optimal control. The method is based on solving optimal open loop control problems on a finite horizon with a sampling of the global value function along the generated trajectories. For the interpolation we choose a kernel orthogonal greedy strategy, because these methods are able to produce extreme sparse surrogates and enable rapid evaluations in high dimensions. Two numerical examples prove the performance of the approach and show that the method is able to deal with high-dimensional feedback control problems, where the dimensionality prevents the approximation by most existing methods.

@article{Schmidt2018f, abstract = {Dealing with high-dimensional feedback control problems is a difficult task when the classical dynamic programming principle is applied. Existing techniques restrict the application to relatively low dimensions since the discretizations typically suffer from the curse of dimensionality. In this paper we introduce a novel approximation technique for the value function of an infinite horizon optimal control. The method is based on solving optimal open loop control problems on a finite horizon with a sampling of the global value function along the generated trajectories. For the interpolation we choose a kernel orthogonal greedy strategy, because these methods are able to produce extreme sparse surrogates and enable rapid evaluations in high dimensions. Two numerical examples prove the performance of the approach and show that the method is able to deal with high-dimensional feedback control problems, where the dimensionality prevents the approximation by most existing methods.}, added-at = {2021-09-29T14:33:27.000+0200}, author = {Schmidt, A. and Haasdonk, Bernard}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2170332c3f0ced359dd0fcfb339ab061b/britsteiner}, doi = {https://doi.org/10.1016/j.ifacol.2018.03.053}, interhash = {4bfa5b3c1d35696d5b7b3d202217e601}, intrahash = {170332c3f0ced359dd0fcfb339ab061b}, issn = {2405-8963}, journal = {IFAC-PapersOnLine}, keywords = {Kernel anm approximation, control, dynamic feedback greedy ians optimal principle, programming techniques}, note = {9th Vienna International Conference on Mathematical Modelling}, number = 2, owner = {santinge}, pages = {307--312}, timestamp = {2021-09-29T12:35:04.000+0200}, title = {Data-driven surrogates of value functions and applications to feedback control for dynamical systems}, url = {http://www.sciencedirect.com/science/article/pii/S2405896318300570}, volume = 51, year = 2018 }