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

Area of Science:

• Complex Systems
• Statistical Physics
• Computational Physics

Background:

• Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.
• Controlling SOC phenomena, like avalanches, is crucial for understanding and managing complex systems.
• Existing control methods often lack explicit optimization strategies balancing system dynamics and intervention costs.

Purpose of the Study:

• To develop and apply a dynamical programming approach for controlling the directed abelian Dhar-Ramaswamy model.
• To establish an optimal control strategy by solving the Bellman equation.
• To benchmark heuristic control methods for larger systems against the derived optimal solution.

Main Methods:

• Utilized dynamical programming to formulate the control problem.
• Employed numerical algorithms to solve the Bellman equation for optimal control.
• Applied the optimal solution as a benchmark to evaluate heuristic strategies.

Main Results:

• Characterized the optimal control solution via the Bellman equation.
• Provided a benchmark for assessing the performance of heuristic control methods on larger systems.
• Demonstrated a novel optimization-based approach for controlling SOC.

Conclusions:

• The dynamical programming approach offers a principled way to control SOC.
• This method explicitly considers the trade-off between avalanche size and intervention cost.
• The findings pave the way for advanced control schemes in complex systems exhibiting SOC.