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Sub-Optimality Bound on a Gradient Method for Iterative Distributed Control Synthesis

A previous paper introduced an online gradient method to iteratively update local controllers for improved performance. In this paper we modify that method to get an offline method for distributed control synthesis. The complexity of the method is linear in the number of neighbors to each agent.

Since the controllers are constructed to be distributed and the method is an iterative scheme, the controllers will always be sub-optimal compared to a centralized controller. We describe a method to calculate bounds of the sub-optimality of the controllers, using the same variables that take part in the update scheme.