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Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities. (English) Zbl 1207.37054
In this paper, a distributed leader-follower flocking algorithm for multi-agent dynamical systems has been developed and analyzed, which considers the case in which the group has one virtual leader and the asymptotic velocity is time-varying. The proposed distributed leader-follower algorithm considers the case in which the group has one virtual leader with time-varying velocity. For each agent i, 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 i 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. It has been proved that although each informed agent can only obtain partial information about the leader, the velocity of the whole group converges 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. It has been the goal of this paper to analyze different flocking algorithms by using tools from non-smooth analysis in combination with ideas from the study of synchronization in complex systems. The leader-follower algorithm considered in this paper fall into the category of free-flocking where no obstacles are considered. 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 $\alpha$-lattice.
##### MSC:
 37N35 Dynamical systems in control