Distributed flocking of lagrangian systems with global connectivity maintenance

Distributed control strategies with connectivity maintenance are proposed for addressing connected flocking of a team of lagrangian systems. First, a completely distributed estimation strategy is devised for estimating the algebraic connectivity, i.e., the second smallest eigenvalue of graph Laplacian, as well as the corresponding eigenvector. Furthermore, based on the estimated parameters, a cooperative flocking algorithm is developed which could steer the agents to the desired flocking motion and to keep the algebraic connectivity to be bounded below by a positive number, which guarantees global network connectivity preservation during maneuvers. Different from the local connectivity maintenance method which keeps some fixed edges for all time, the proposed algorithm guarantees the connectivity while allowing any existing edge to be broken, which enhances the flexibility and adaptability for the overall system. Finally, nontrivial simulation results are presented to show the effectiveness of the proposed control algorithm.