Dynamical programming approach for controlling the directed Abelian Dhar-Ramaswamy model

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.