Distributed Optimization for Model Predictive Control of Linear-Dynamic Networks

A linear-dynamic network consists of a directed graph in which the nodes represent subsystems and the arcs model dynamic couplings. The local state of each subsystem evolves according to discrete linear dynamics that depend on the local state, local control signals, and control signals of upstream subsystems. Such networks appear in the model predictive control (MPC) of geographically distributed systems such as urban traffic networks and electric power grids. In this correspondence, we propose a decomposition of the quadratic MPC problem into a set of local subproblems that are solved iteratively by a network of agents. A distributed algorithm based on the method of feasible directions is developed for the agents to iterate toward a solution of the subproblems. The local iterations require relatively low effort to arrive at a solution but at the expense of high communication among neighboring agents and with a slower convergence rate.