Designing communication networks to decompose network control problems

The pressure from today's economic and energy markets demands further distribution of decision making in large, dynamic networks. To this end, distributed model predictive control (MPC) divides the task of operating a dynamic network into a set of small, localized subtasks, one for each distributed control agent. To guide the decomposition of the overall task, which plays a central role in the quality of the operation yielded by the distributed agents, this paper proposes a model for problem decomposition based on the design of agent communication networks. The model gives rise to the communication-network design problem: A bicriteria optimization problem whose objectives are the maximization of the influence perceived by the agents and the minimization of the communication cost. The benefit of the model is the potential to concentrate the effort of implementing distributed MPC, and measuring its actual performance, on a reduced number of decompositions, namely those that are Pareto efficient for the model. The paper gives an account of related work, including the computational complexity of finding Pareto efficient solutions, an integer programming formulation, and families of valid inequalities. Its main contribution is the demonstration that the model can be effective, meaning that Pareto efficient solutions to the model tend to induce efficient problem decompositions. The experimental evidence was gathered by applying the model to decompose control problems of two representative networks, namely arrays of pendulums and electric power networks, and measuring the quality of the operation delivered by the distributed control agents.