Boundary Control for Wildfire Mitigation

TL;DR

This paper develops boundary control strategies using PDE models to mitigate wildfires by stabilizing temperature in protected regions, with adaptive methods for unknown wind conditions, supported by simulations.

Contribution

It introduces boundary control methods for wildfire mitigation modeled by PDEs, including adaptive control for unknown wind velocity, a novel approach in this context.

Findings

Boundary control guarantees exponential temperature convergence under known wind.

Adaptive boundary control ensures asymptotic temperature stabilization with unknown wind.

Numerical simulations validate the effectiveness of the proposed control strategies.

Abstract

In this paper, we propose a feedback control strategy to protect vulnerable areas from wildfires. We consider a system of coupled partial differential equations (PDEs) that models heat propagation and fuel depletion in wildfires and study two cases. First, when the wind velocity is known, we design a Neumann-type boundary controller guaranteeing that the temperature of some protected region converges exponentially, in the $L^2$ norm, to the ambient temperature. Second, when the wind velocity is unknown, we design an adaptive Neumann-type boundary controller guaranteeing the asymptotic convergence, in the $L^2$ norm, of the temperature of the protected region to the ambient temperature. In both cases, the controller acts along the boundary of the protected region and relies solely on temperature measurements along that boundary. Our results are supported by numerical simulations.