Robustness Properties of Distributed Configurations in Multi-Agent Systems1

This paper considers a distributed LQR design framework for a multi-agent network consisting of identical dynamically decoupled agents. A systematic method is presented for computing the performance loss of various distributed control configurations relative to the performance of the optimal centralized controller. Necessary and sufficient conditions have been derived for which a distributed control configuration pattern arising from the optimal centralizing solution does not entail loss of performance if the initial vector lies in a certain subspace of state-space which is identified. It was shown that these conditions are always satisfied for systems with communication/control networks corresponding to complete graphs with a single link removed. A procedure is extended for analyzing the performance loss of an arbitrary distributed configuration which is illustrated by an exhaustive analysis of a network consisting of agents described by second-order integrator dynamics. Presented results are useful for quantifying performance loss due to decentralization and for designing optimal or near-optimal distributed control schemes.