A Study of Synchronization and Group Cooperation Using Partial Contraction Theory

Abstract

Synchronization, collective behavior, and group cooperation have been the object of extensive recent research. A fundamental understanding of aggregate motions in the natural world, such as bird flocks, fish schools, animal herds, or bee swarms, for instance, would greatly help in achieving desired collective behaviors of artificial multi-agent systems, such as vehicles with distributed cooperative control rules. In [38], Reynolds published his well-known computer model of “boids,” successfully forming an animation flock using three local rules: collision avoidance, velocity matching, and flock centering. Motivated by the growth of colonies of bacteria, Viscek et al.[55] proposed a similar discrete-time model which realizes heading matching using information only from neighbors. Viscek’s model was later analyzed analytically [16, 52, 53]. Models in continuous-time [1, 22, 32, 33, 62] and combinations of Reynolds’ three rules [21, 34, 35, 49, 50] were also studied. Related questions can also be found e.g. in [3, 18, 20, 42], in oscillator synchronization [48], as well as in physics in the study of lasers [39] or of Bose-Einstein condensation [17].