Coherence in Large-Scale Networks: The Multi-Scale Effects of Feedback

Abstract:

Problems of coordinated motion of vehicular formations have received much attention lately, especially in the areas of formation flight and so-called vehicular platoons. We investigate fundamental limitations that the use of spatially small-scale (i.e. local) feedback control has on the coherence of large formations that are subjected to stochastic disturbances. The notion of coherence translates roughly into how closely can such formations resemble a solid object, and is unrelated to the notion of string instability. This question is also of interest in the context of naturally occurring swarms, such as birds in flying formations and schools of fish. Similar dynamical phenomena occur in distributed load balancing in parallel processing and consensus-type algorithms.

We examine these dynamical effects using the network topology of regular lattices, and investigate the role of topological dimension. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with dimensions of 3 and 5 being necessary to achieve coherence in consensus and vehicular formations respectively with only local feedback. We show that microscopic error measures that involve only neighboring vehicles scale much more favorably, and in some cases do not suffer from this effect. This phenomenon reflects a fact that in lower spatial dimensions, local stabilizing feedbacks are relatively unable to regulate against spatially large-scale disturbances, resulting in an unregulated, "undulating" type of motion for the entire formation. We point out connections between this analysis and the statistical mechanics of harmonic solids where such phenomena have long been observed, as well as connections with the theory of resistive lattices as has been observed by others.

 

Biography:

Bassam Bamieh is Professor of Mechanical Engineering at the University of California at Santa Barbara. He received his B.Sc. degree in Electrical Engineering and Physics from Valparaiso University (Valparaiso, IN) in 1983, and his M.Sc. and PhD degrees in Electrical and Computer Engineering from Rice University (Houston, TX) in 1986 and 1992 respectively. Prior to joining UCSB in 1998, he was an Assistant Professor in the Department of Electrical and Computer Engineering and the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign (1991-98).

Professor Bamieh's research interests are in the general area of Control and Dynamical Systems, as well as the applications of systems and feedback techniques in several physical and engineering systems. Aside from basic research on the theory of Robust and Optimal Control, his group carries out several research activities including the theory of quantum control, distributed control and dynamical systems, shear flow transition and turbulence, and the use of feedback in thermoacoustic energy conversion devices.

Professor Bamieh has co-authored over 100 refereed publications in Systems and Controls and allied fields. He has received several awards and honors for his research, including an IEEE Control Systems Society G. S. Axelby Outstanding Paper Award, an AACC Hugo Schuck Best Paper Award, and a National Science Foundation CAREER award. He was elected a Distinguished Lecturer of the IEEE Control Systems Society (2005), and a Fellow of the IEEE (2008) with the citation "For contributions to robust, sampled-data and distributed control".