A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems
october, 2021
Publication type:
Paper in peer-reviewed journals
Journal:
Monte-Carlo methods and applications., vol. 27 (4), pp. 347-371
HAL:
arXiv:
Keywords :
Ornstein-Uhlenbeck processes; probabilistic representation of
PDEs; time-reversal of diffusion; stochastic control; HJB equation;
regression Monte-Carlo scheme; demand-side management.
Abstract:
We propose a fully backward representation
of semilinear PDEs with application to stochastic control.
Based on this, we develop a fully backward Monte-Carlo scheme allowing to
generate the regression grid, backwardly in time, as the value function is
computed. This offers two key advantages in terms of computational
efficiency and memory. First, the grid is generated adaptively in the areas of interest and second, there is no need to store the entire grid.
The performances of this technique are compared in simulations
to the traditional Monte-Carlo forward-backward approach
on a control problem of thermostatic loads.
BibTeX:
@article{Izy-Oud-Rus-2021,
author={Lucas Izydorczyk and Nadia Oudjane and Francesco Russo },
title={A fully backward representation of semilinear PDEs applied to
the control of thermostatic loads in power systems },
doi={10.1515/mcma-2021-2095 },
journal={Monte-Carlo methods and applications. },
year={2021 },
month={10},
volume={27 (4) },
pages={347--371},
}