A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems

Lucas Izydorczyk, Nadia Oudjane and Francesco Russo
to appear
Publication type:
Paper in peer-reviewed journals
Journal:
Monte-Carlo methods and applications.
arXiv:
assets/images/icons/icon_arxiv.png 2104.13641
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-2100,
    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 },
    journal={Monte-Carlo methods and applications. },
    year={to appear },
    month={4},
}