Distributed leader–follower flocking control for multi-agent dynamical systems with time-varying velocities

Using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions, velocity consensus and navigation feedback, a distributed leader–follower flocking algorithm for multi-agent dynamical systems with time-varying velocities is developed where each agent is governed by second-order dynamics. The distributed leader–follower algorithm considers the case in which the group has one virtual leader with time-varying velocity. For each agent ii, this algorithm consists of four terms: the first term is the self nonlinear dynamics which determines the final time-varying velocity, the second term is determined by the gradient of the collective potential between agent ii and all of its neighbors, the third term is the velocity consensus term, and the fourth term is the navigation feedback from the leader. To avoid an impractical assumption that the informed agents sense all the states of the leader, the new designed distributed algorithm is developed by making use of observer-based pinning navigation feedback. In this case, each informed agent only has partial information about the leader, yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents, having the leader’s position information, follows the trajectory of the leader asymptotically. Finally, simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis. Surprisingly, it is found that the local minimum of the potential function may not form a commonly believed αα lattice.