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

TL;DR

This paper introduces a fully backward Monte-Carlo method for solving semilinear PDEs in stochastic control, improving efficiency and memory use, demonstrated on thermostatic load control in power systems.

Contribution

It presents a novel fully backward Monte-Carlo scheme that adaptively generates the regression grid, reducing memory requirements and computational costs in solving semilinear PDEs.

Findings

Enhanced computational efficiency over traditional methods

Adaptive grid generation improves focus on relevant regions

Successful application to thermostatic load control

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.