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We study fundamental performance limitations of distributed feedback controlin large-scale networked dynamical systems. Specifically, we address thequestion of whether dynamic feedback controllers perform better than static(memoryless) ones when subject to locality constraints. We consider distributedlinear consensus and vehicular formation control problems modeled over toriclattice networks. For the resulting spatially invariant systems we study thelarge-scale asymptotics (in network size) of global performance metrics thatquantify the level of network coherence. With static feedback from relativestate measurements, such metrics are known to scale unfavorably in lattices oflow spatial dimensions, preventing, for example, a 1-dimensional string ofvehicles to move like a rigid object. We show that the same limitations ingeneral apply also to dynamic feedback control that is locally of first order.This means that the addition of one local state to the controller gives asimilar asymptotic performance to the memoryless case. This holds unless thecontroller can access noiseless measurements of its local state with respect toan absolute reference frame, in which case the addition of controller memorymay fundamentally improve performance. In simulations of platoons with 20-200vehicles we show that the performance limitations we derive manifest asunwanted accordion-like motions. Similar behaviors are to be expected in anynetwork that is embeddable in a low-dimensional toric lattice, and the samefundamental limitations would apply. To derive our results, we present ageneral technical framework for the analysis of stability and performance ofspatially invariant systems in the limit of large networks.

On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks