Dynamic dual decomposition for distributed control

We show how dynamic price mechanisms can be used for decomposition and distributed optimization of feedback systems. A classical method to handle large scale optimization problems is dual decomposition, where the coupling between sub-problems is relaxed using Lagrange multipliers. These variables can be interpreted as prices in a market mechanism serving to achieve mutual agreement between solutions of the sub-problems. In this paper, the same idea is used for decomposition of feedback systems, with dynamics in both decision variables and prices. We show how the prices can be used for a decentralized test, to verify that the global feedback system stays within a prespecified distance from optimality.