Flocking with informed agents. (Cucker, Felipe; Huepe, Cristian)

MathS In Action 1, No. 1, 1-25, electronic only (2008).
Abstract: Two similar Laplacian-based models for swarms with informed agents are proposed and analyzed analytically and numerically. In these models, each individual adjusts its velocity to match that of its neighbors and some individuals are given a preferred heading direction towards which they accelerate if there is no local velocity consensus. The convergence to a collective group swarming state with constant velocity is analytically proven for a range of parameters and initial conditions. Using numerical computations, the ability of a small group of informed individuals to accurately guide a swarm of uninformed agents is investigated. The results obtained in one of our two models are analogous to those found for more realistic and complex algorithms for describing biological swarms, namely, that the fraction of informed individuals required to guide the whole group is small, and that it becomes smaller for swarms with more individuals. This observation in our simple system provides insight into the possibly robust dynamics that contribute to biologically effective collective leadership and decision-making processes. In contrast with the more sophisticated models mentioned above, we can describe conditions under which convergence to consensus is ensured.

Flocking of multi-agent systems with a dynamic virtual leader (Shi, Hong; Wang, Long; Chu, Tianguang)

Int. J. Control 82, No. 1, 43-58 (2009). ISSN 0020-7179; ISSN 1366-5820 
Abstract: This paper considers the flocking problem of a group of autonomous agents moving in Euclidean space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighbouring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighbouring agents and the external reference signal (or ‘virtual leader’). Then we prove that, if the acceleration of the virtual leader is known, then each agent can follow the virtual leader, and the convergence rate of the centre of mass (CoM) can be estimated; if the acceleration is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, thus the flocking motion can be obtained. However, in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to illustrate our theoretical results.