Multi-Agent Interval Consensus with Flocking Dynamics

In this paper, we investigate the interval consensus for a network of agents with flocking dynamics, where each agent imposes an interval constraint on its preferred consensus values. Specifically, we work on two different frameworks, viz., the first one that the node states are constrained in their own constraint intervals and the second one that the node states are constrained in their neighbors' constraint intervals. For both frameworks, we provide a complete solution to the equilibrium seeking problem by resolving a system of nonlinear equations. It is proved that if the underlying graph is strongly connected and the intersection of constraint intervals is empty, then there exists a unique equilibrium point; and if the intersection is non-empty, then there exist multiple equilibrium points. We also establish several conditions for the local stability of the unique equilibrium point or local constraint consensus by invoking Lyapunov's indirect method. In addition, we show in two special cases that global convergence to the unique equilibrium point or state consensus can be guaranteed by employing Lyapunov stability theory and robust analysis techniques.