A dynamical programming approach for controlling the directed abelian Dhar-Ramaswamy model

TL;DR

This paper applies a dynamic programming approach to control the directed abelian Dhar-Ramaswamy model, optimizing interventions to manage avalanches in a self-organized critical system, and compares heuristic strategies to the optimal solution.

Contribution

It introduces the first optimization-based control scheme for self-organized criticality models, explicitly balancing avalanche size and intervention costs.

Findings

Optimal control solutions via Bellman equation are obtained.

Heuristic strategies are evaluated against the optimal benchmark.

The approach provides a framework for controlling critical systems.

Abstract

A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the optimal solution of the problem is characterized by the solution of the Bellman equation obtained by numerical algorithms. Second, the solution is used as a benchmark to value how far from the optimum other heuristics that can be applied to larger systems are. This approach is the first attempt on the direction of schemes for controlling self-organized criticality that are based on optimization principles that consider explicitly a tradeoff between the size of the avalanches and the cost of intervention.